Throughout this verse, we are taught not to shoulder all the burdens on ourselves. Instead, we should give them all to God because God Cares for us. 
How do we cast our care on God? It all comes down to trusting the promises made by God in His precious word and believing that He will fulfill all of them. He will answer our prayers, and He will do so in His own time and in His own way - for our greater good and for His greater glory. All we need to do is to acknowledge, with humility of heart, our lack of abilities, and to accept His offer to cast all our cares on Him, knowing, as we do, that He cares for us and is able to help us in times of need.
Having faith in the truth of God's Word is something that we will never doubt, for what He has promised, He will fulfill. May we humble ourselves at the mighty hand of God so that He may exalt us at the proper time. May we cast all our worries and anxiety on Him because no matter what, He cares for each of His children.

Dear Heavenly Father, please forgive me for being too self-sufficient for far too long. For too long, I have tried to solve all my problems on my own, relying on my own strength and wisdom. Father, that You care so much to allow me to cast all my burdens upon You and so that I can give You all the hurts, disappointments, and worries that now seem to be flooding my life. In Your presence, I am assured that You will carry each and every anxiety and pain of mine. 
Dear Father, I confess to you that I am weak. However, I praise You for Your amazing strength that I may draw upon today and in the days to come.
In Jesus's name I pray. Amen.