Psalm 3

Salvation is from God. Yair (Translation and Commentary) on the Book of Psalms (10 February, 2015, 21 Shevet, 5775)

King David fled from his son, Absalom, who had rebelled against him. David was being punished for having sinned. Nevertheless David repented and was forgiven. God helped him. If David could repent and be forgiven then so can we and the rest of the world!
Duration: 10.03 minutes

Psalms 3:
A PSALM OF  DAVID WHEN HE FLED FROM ABSALOM, HIS SON ,

Some Psalms begin with, A PSALM OF  DAVID others say, FOR DAVID, A PSALM. 
There are versions (such as the Hebrew language editions) where this opening is numbered as verse 1, in others it is not numbered but the number 1 is given to the next verse. This explains the discrepancy of one number that may be found in some references.
S.   R.  Hirsch explains that David sometimes composed his Psalms as a result of Divine Inspiration and in other cases he used the act of composition as a means to reach up to the necessary level.  So to, we can use music and poetry to draw closer to the Almighty and those who are so gifted may even achieve a degree of inspiration through their own composition. The Prophet Elisha  for example when requested to prophesy replied, "But now bring me a minstrel." And it came about, when the minstrel played, that the hand of the LORD came upon him (2-Kings 3:15).
S.R. Hirsch points out that this Psalm 3 comes after Psalm 2 in which the peoples of the world are summoned to acknowledge the authority of the future Messiah descendant of David who will impose a universal code of morality on all mankind.  David himself however had transgressed this very code by taking the woman of another (2-Samuel chapter 11). The revolt of Absalom came upon him as punishment for his sin (2-Samuel 12:11). His enemies took advantage of his predicament to close in for the kill. David however repented. In this Psalm we see that David knows God will save him out of his present trouble. 

David repented and was forgiven and helped by God. We can also repent and we shall be helped by God. So too, the Peoples of the World will be expected to repent and if they do, God will help them!

1 LORD, how my opponents have multiplied! Many have risen against me.

2 Many say of my being, there will be no salvation for him from God. Selah.

Many of the self-righteous apparently claimed that because David  had sinned God had abandoned him.  

SELAH is of uncertain meaning. It had musical implications and also connoted "upliftment", "eternity", and/or "reflection".   It may also have meant  "true", similar to the word "Amen".

3 But you, LORD, are a shield for me; my honor, and the uplifter of my head.

4  I shall call unto the LORD and HE shall answer me from HIS Holy Mount. Selah.
The KJV renders this verse:
I CRIED UNTO THE LORD WITH MY VOICE, AND HE HEARD ME OUT OF HIS HOLY HILL. SELAH.

The Hebrew word translated here by us as "HE shall call"  is "AKRA" from the root "KRA". This indeed is the source of the English word "cry". The two words in English and Hebrew are practically the same. Compare this to the conventional etymology:

cry (v.)
http://www.etymonline.com/index.php?term=cry
early 13c., "beg, implore," from Old French crier, from Vulgar Latin *critare, from Latin quiritare "to wail, shriek" (source of Italian gridare, Old Spanish cridar, Spanish and Portuguese gritar), which is of uncertain origin; perhaps a variant of quirritare "to squeal like a pig," from *quis, echoic of squealing, despite ancient folk etymology that traces it to "call for the help of the Quirites," the Roman constabulary. The meaning was extended 13c. to weep, which it largely replaced by 16c. Related: Cried; crying.

The alternate English word that we chose is "call". This in fact is also derived from Hebrew word "KOL" meaning voice and in verbal form "give voice", i.e. call.

call (v.)
http://www.etymonline.com/index.php?allowed_in_frame=0&search=call&searchmode=none
Old English ceallian "to call, shout," less common than clipian; replaced by related Old Norse kalla "to cry loudly," from Proto-Germanic *kall- (cognates: Dutch kallen "to talk," Old High German kallon "to call"), from PIE root *gal- (2) "to call, scream, shriek, shout" (cognates: Sanskrit garhati "bewail, criticize;" Latin gallus "cock;" Old High German klaga, German Klage "complaint, grievance, lament, accusation;" Old English clacu "affront;" Old Church Slavonic glasu "voice," glagolu "word;" Welsh galw "call"). Related: Called; calling.

HIS HOLY MOUNT. This is referring to the  Temple Mount.  Even though the Temple had not yet been built it was already recognized as a holy site.

5 I lay me down and I slept; I awoke for the LORD supported me.

 S.R. Hirsch points out that David was fleeing from his son and beset with enemies all around, all striving to physically destroy him and all he stood for. The simple act of falling asleep and awaking refreshed was a source of inspiration for him in time of dire trouble. Sleep can have great therapeutic value.

6 I shall not fear the myriads of people who are set around  against me.

David was one of the greatest men who ever lived yet numerous people thirsted for his blood.  So too, we should not be disheartened if we encounter opposition or difficulties.

7 Arise LORD; save me, MY God. For you have struck all of my enemies on the cheek, the teeth of the ungodly you have broken.

 Teeth are very important: - As someone who now lacks many of his own,  I can vouch for it.  A great many people in the UK and Australia before WW2 and in the following generations had bad teeth.  Nowadays the situation is different.  In Israel people have good teeth and generally look after them.  In Biblical Law, a master who caused the loss of a single tooth of his slave had to set the slave free (Exodus 21:27).  This shows how important teeth are.
Not only teeth but a persons health in general is a God-given blessing  that we should endeavor to take good care of.
 If a single tooth is worth so much how much more should we care for the rest of our body!
I suppose people of a mystical bent could consider loosing one's teeth an atonement parallel to being set free?
On the other hand it could also be a punishment.
We find other verses where breaking the teeth of the wrongdoers is recalled
cf.  # O God, break the teeth in their mouths;   tear out the fangs of the young lions, O Lord! # (Psalms 58:6).
Perhaps both possibilities are applicable? Punishment and atonement together via the dentist? or lack of one?

8 To the LORD does salvation belong; on your people [bestow] YOUR blessing. Selah.

Israel is the people of God. We should never forget this.

The People of God are the Israelite Nations meaning the Jews of Judah and Benjamin  and the Lost Ten Tribes.