Many times in my life I've heard people offer someone the advice "give it all to Jesus." "Give your problems to Him." "Give your worries to Him." I had no idea what that meant or how you did that. Google wasn't terribly helpful.
Eventually I tried to imagine how He would respond if I confessed I had no idea how to give Him my burdens. The response I came up with was, "You just ask Me. Ask Me to take it, and let go of it. Stop worrying. Trust Me." A scene came to mind. He was kneeling in front of me with an open backpack I had been carrying that was filled with stones. He handed me each one and asked what problem, worry or fear it represented. I told Him what it was and asked if He would take it from me. He said yes, and took each one from me until my backpack was empty.
So now when I have a burden, I imagine myself holding a stone with Jesus standing in front of me. I say, "Jesus, I'm worried about ________________. Will You take this burden from me?" He says yes and takes it from me. I demonstrate my trust in Him by not worrying about it anymore.
I made a list of burdens I've given to Him so I can remind myself what I'm not going to worry about, and so I can see the results as time goes by. I have been pretty good about not stressing over most of them, trusting them to His care - although on occasion I've tried to take one back, only to have to let go of it again!
My testimony of this concept has been greatly strengthened in the last few months. I was very worried about a certain confrontation happening. Twice now opportunities for that confrontation to happen have arisen. Both times I gave Him the burden and stopped worrying about it (though I did occasionally remind Him I was counting on Him!). The opportunities were averted both times. His solutions were far better than any ideas I had come up with own my own. (And He's probably the only one who could have averted them anyway!)
Now that I have had these experiences, I know for sure that giving Him my burdens is a much better solution than worrying, stressing, and trying to solve my problems myself! It's better to let go of the anxiety and stress and trust that everything is in His hands.