Why are you cast down, O my soul,
and why are you in turmoil within me?
Hope in God; for I shall again praise him,
my salvation and my God.
So, why do we have turmoil (and we all do, don't we)? Because most of the time we aren't hoping in God but in other things (people, our abilities, success, money, you name it.....) that can't deliver and/or are unattainable. Only God can satisfy our every need, and only He won't disappoint, only He will never let us down.
So, what does it look like to Hope in God? I think v. 1-2 give the answer:
As a deer pants for flowing streams,
so pants my soul for you, O God.
2My soul thirsts for God,
for the living God.
Hoping in God means wanting Him more than anything else, and continually seeking after Him with everything we are. When we do this, we will never be disappointed, and turmoil will turn into praise.