The peace of God happens when you obey Him. What I mean is, when you walk with Him, He lets you live in His peace. If Christians truly believed that God had their best interests at heart, as His children, then they wouldn't worry about getting their needs met. And tell me if I'm wrong, but if we all had our needs perfectly supplied, wouldn't we have all the peace we ever needed?
"Thou wilt keep Him in perfect peace, whose mind is stayed on Thee: because He trusteth in Thee." (Isaiah 26:3)
God's peace isn't simply the absence of conflict. Conflict and chaos is (as in, extant). It's a negative tide that will encroach and fill and flow in if you let it. As we live in this world, "the flesh lusteth against the Spirit, and the Spirit against the flesh: and these are contrary the one to the other. This is the...doublebeing? (As opposed to "doublespeak" and "doublethink".) that we live in. It's the natural order of things. And if it were to cease, it would be Heaven. This is why God gives us His peace in the midst. A taste of that which we cannot have in full purely by virtue of existing in a fallen space.
When it says in Isaiah that, if our mind were "stayed" on God, we would have perfect peace, is it really that simple? Uh, it actually is. But simple and easy are two different things. We also deal with the accruing consequences of past actions that become the part of the threatening tide.
"And the God of peace shall bruise Satan under your feet shortly. The grace of our Lord Jesus Christ be with you. Amen." (Romans 16:20)
Now, assuming you've dealt with any negative spiritual forces encroaching upon your station, God's peace will slowly diffuse with whatever portion of your mind you choose to devote to Him. And remember "He that is faithful in that which is least is faithful also in much..." (Luke 16:10). If you parse out your day and your mind and deliberately commit certain aspects of such to God, He will infuse each with His peace. Needs are easily supplied. God's peace is something that's impossible to attain unless directly from Him. He's good for it.
In closing, if all you can do is speak back to God what He's spoken to you in His word, that's a good place to start.