We start at the very first Psalm. I'm sure I have missed some verses, but I've tried my best with the time I have. I will try and go in order, and I encourage you to please follow along with your (hopefully translated from the Textus Receptus) Bible.
I would also encourage you to read the surrounding contexts in these verses, when applicable. I don't have the space to post the whole Psalms, and a lot of the time the entire context really clarifies things. Thanks!
 And he shall be like a tree planted by the rivers of water, that bringeth forth his fruit in his season; his leaf also shall not wither; and whatsoever he doeth shall prosper.
 The ungodly are not so: but are like the chaff which the wind driveth away.
 Therefore the ungodly shall not stand in the judgment, nor sinners in the congregation of the righteous.
 For the LORD knoweth the way of the righteous: but the way of the ungodly shall perish.
The key thing to take away from here is verse 6. The ungodly shall perish. What does perish mean in the Hebrew? Let's take a look!
A primitive root; properly to wander away, that is lose oneself; by implication to perish (causatively, destroy): - break, destroy (-uction), + not escape, fail, lose, (cause to, make) perish, spend, X and surely, take, be undone, X utterly, be void of, have no way to flee.
You guessed it, it means destroy! Be void of! Fail, lose! When does perish mean burn forever?
Also, note the references to trees bringing fruit, leaves not withering, and chaff being driven away. These are themes throughout the whole Bible. Jesus talks plenty about trees, vineyards, and fruits. The bad trees wither away! They are destroyed, they die off.
 For thou art not a God that hath pleasure in wickedness: neither shall evil dwell with thee.
 The foolish shall not stand in thy sight: thou hatest all workers of iniquity.
 Thou shalt destroy them that speak leasing: the LORD will abhor the bloody and deceitful man.
God hates wickedness, evil shall not dwell with Him. He will destroy them. If someone dies from a heart attack let's say, is that God destroying them? No, God destroying them is Him putting His judgment upon them. Casting them into the lake of fire, which is the second death. (Rev. 20:14)
The word "destroy" here is the exact word used for "perish" in Psalm 1:6.
 For in death there is no remembrance of thee: in the grave who shall give thee thanks?
Does David say in a burning "hell" there is no rememberance of God? Let's think this out here. If one is saved, they're with the Lord forever. So David isn't talking about Christians in this verse, because Christians will always be with the Lord. He can only be referring to one other group of people, right? He doesn't say they're in "hell," either. He says they're in the grave. Besides, would people in a burning "hell" forget Who put them there?
 Oh let the wickedness of the wicked come to an end; but establish the just: for the righteous God trieth the hearts and reins.
I think this verse is very clear. "Let the wickedness of the wicked come to an end." If wicked people are in "hell," aren't they still around? Haven't they not come to an end? We know this verse talks of the eternal fate of a person, especially because God establishes His people forever. A few verses down, talking of the wicked,
 He made a pit, and digged it, and is fallen into the ditch which he made.
Sounds to me like the wicked go into the pit, the grave.
 Thou hast rebuked the heathen, thou hast destroyed the wicked, thou hast put out their name for ever and ever.
 O thou enemy, destructions are come to a perpetual end: and thou hast destroyed cities; their memorial is perished with them.
 But the LORD shall endure for ever: he hath prepared his throne for judgment.
"Thou hast destroyed the wicked, thou hast put out their name for ever and ever." Destroyed and put out their name! What does someone do to a fire at the end of a campfire? They put it out! God will "put out" the wicked, forever! It further says in verse 7 that God endures forever. It's contrasted with how the wicked are put out. God endures forever, the wicked don't.
 Have mercy upon me, O LORD; consider my trouble which I suffer of them that hate me, thou that liftest me up from the gates of death:
I used this verse in this study to show that the gates of death is the thing we are facing, not the gates of a burning inferno. I went into this in part 1 of my study.
 The heathen are sunk down in the pit that they made: in the net which they hid is their own foot taken.
 The wicked shall be turned into hell, and all the nations that forget God.
 For the needy shall not alway be forgotten: the expectation of the poor shall not perish for ever.
So the heathen go down into the pit (a most often recurring theme, as we see already), they are turned into hell (sheol, the grave), but the needy are not forgotten! The expectation of the poor shall not perish forever! Doesn't this say that the wicked DO perish forever? Combined with every other verse (I have well over 80 now), I'd say this is the case.
 Break thou the arm of the wicked and the evil man: seek out his wickedness till thou find none.
 The LORD is King for ever and ever: the heathen are perished out of his land.
Again, God is King forever, the heathen perish. They are not forever. A burning inferno would mean that the wicked are immortal too. Are you starting to see how "hell" does not line up with Scripture?
 Upon the wicked he shall rain snares, fire and brimstone, and an horrible tempest: this shall be the portion of their cup.
I think this is talking of God's judgment on the wicked. Fire and brimstone = lake of fire. (Rev 19:20) The lake of fire is the second death. (Rev 20:14)
 The LORD shall cut off all flattering lips, and the tongue that speaketh proud things:
Hmm, cut off. What does this mean? Thankfully, the Lord has lead me to another Psalm that defines it. I will skip ahead just to immediately define what this phrase means.
 Free among the dead, like the slain that lie in the grave, whom thou rememberest no more: and they are cut off from thy hand.
The ones that are "cut off" are ones that God has done away with. Ones He has left slain in the graves, that He remembers no more! Just to solidify this point, the definition of "cut off:"
A primitive root; to cut (off, down or asunder); by implication to destroy or consume; specifically to covenant (that is, make an alliance or bargain, originally by cutting flesh and passing between the pieces): - be chewed, be con- [feder-] ate, covenant, cut (down, off), destroy, fail, feller, be freed, hew (down), make a league ([covenant]), X lose, perish, X utterly, X want.
It means to destroy or perish! To consume! The Lord will "cut off," or destroy the wicked. It's all throughout the Bible, and I'm trying my best to show you.
 Now know I that the LORD saveth his anointed; he will hear him from his holy heaven with the saving strength of his right hand.
 Some trust in chariots, and some in horses: but we will remember the name of the LORD our God.
 They are brought down and fallen: but we are risen, and stand upright.
 Save, LORD: let the king hear us when we call.
The Lord saves His people, the ones that don't trust in Him are brought down and fallen. After many other supporting verses, I can't help to think that brought down refers to down into the grave/pit. When I read fallen, I think of someone that has died. Here's the Hebrew:
A primitive root; to fall, in a great variety of applications (intransitively or causatively, literally or figuratively): - be accepted, cast (down, self, [lots], out), cease, die, divide (by lot), (let) fail, (cause to, let, make, ready to) fall (away, down, -en, -ing), fell (-ing), fugitive, have [inheritamce], inferior, be judged [by mistake for H6419], lay (along), (cause to) lie down, light (down), be (X hast) lost, lying, overthrow, overwhelm, perish, present (-ed, -ing), (make to) rot, slay, smite out, X surely, throw down.
It can be defined as cease, die, fail, fall, perish, rot. Look familiar?
 Thine hand shall find out all thine enemies: thy right hand shall find out those that hate thee.
 Thou shalt make them as a fiery oven in the time of thine anger: the LORD shall swallow them up in his wrath, and the fire shall devour them.
A fiery oven: the time of judgment, the lake of fire. When the tares are gathered into the oven and are burned up. The Lord will swallow them up in His wrath, and fire shall devour them. Devour! What does devour mean?
A primitive root; to eat (literally or figuratively): - X at all, burn up, consume, devour (-er, up), dine, eat (-er, up), feed (with), food, X freely, X in . . . wise (-deed, plenty), (lay) meat, X quite.
To burn up! This is huge. To consume! We're talking about a fire that burns up and consumes them. Does an eternal hell burn something up? Nope, it just burns something. Does it consume something? Not if it's continually burning! The fire God sends on the wicked is a consuming one that burns up everyone in its path. Nobody survives it.
 Because they regard not the works of the LORD, nor the operation of his hands, he shall destroy them, and not build them up.
God will destroy the wicked, and not build them up. They're done.
 O LORD, thou hast brought up my soul from the grave: thou hast kept me alive, that I should not go down to the pit.
 What profit is there in my blood, when I go down to the pit? Shall the dust praise thee? shall it declare thy truth?
God hasn't brought his soul up from a burning inferno, He brought him up from the grave, the pit.
 O love the LORD, all ye his saints: for the LORD preserveth the faithful, and plentifully rewardeth the proud doer.
The Lord preserves the faithful. Ok, we know that. Here's what it means in the Hebrew:
A primitive root; to guard, in a good sense (to protect, maintain, obey, etc.) or a bad one (to conceal, etc.): - besieged, hidden thing, keep (-er, -ing), monument, observe, preserve (-r), subtil, watcher (-man).
To guard in a good sense, to conceal in a bad sense. To keep, preserve. Wouldn't the wicked be concealed in a bad sense if they are kept alive in torment? Yes. The Lord does not preserve the wicked, because Psalm 31 states that He preserves the faithful. By this reasoning it's impossible to have anyone preserved in "hell."
 Behold, the eye of the LORD is upon them that fear him, upon them that hope in his mercy;
 To deliver their soul from death, and to keep them alive in famine.
To deliver their soul from death, not from an eternally burning inferno.
 The face of the LORD is against them that do evil, to cut off the remembrance of them from the earth.
Again we see the term "cut off." Destroyed. This just came to me. If anyone is thinking that this is just talking about the mortal condition of the wicked, remember, the meek inherit the earth. They reign with Christ for 1000 years in Israel, then reign with Him after the wicked are destroyed and New Jerusalem descends.
Alright, I feel that it's time to wrap up this entry. I'd rather make these studies shorter than I have in the past, so that they are easier to read. I hope from this first look into what Psalms says about hell and the wicked is showing you a stark reality: the wicked are burned up by God's fire (the lake of fire) and utterly destroyed.
Part 3 of my study on hell is coming soon! I will address many more verses that I have found in Psalms. Thanks for reading, and as always I welcome your comments and will do my best to answer them.
CLICK HERE FOR PART 3