The Lord is my light and my salvation; whom shall I fear? David asks the question rhetorically, then spends the psalm giving reasons why fear keeps knocking anyway — armies encamping, enemies, false witnesses, even the possibility that his father and mother might forsake him.
So this is not a psalm by someone who has stopped being afraid. It is a psalm by someone conducting an argument with his own fear, out loud, using what he knows about God as the counterweight.
The middle of it contains a request that is easy to skim past. Of all the things he could ask for while under threat — victory, safety, vindication — he asks for one thing: that I may dwell in the house of the Lord all the days of my life, to behold the beauty of the Lord. Under siege, his desire is not primarily rescue. It is nearness.
Then the last two verses turn and speak to himself: Wait on the Lord: be of good courage, and he shall strengthen thine heart: wait, I say, on the Lord. He repeats the instruction because once was not enough, even for the man who wrote it.
That may be the most useful thing here. Faith often looks less like calm and more like telling yourself the truth a second time.