Set your mind right before you go to bed. Start simple. Make sure that you do go to bed, and not lie down on the sofa. Turn down the lights in your bedroom, and light a simple white candle – that has been placed in a sturdy candle-holder on the dresser. Say a prayer as you sit and look at the candle.
If you believe in a god, then you have a head start. You can recite a prayer from a your holy book or oral tradition. Then briefly lay down your main worry for that god to help you release it. Talk about what you think is keeping you from your sleep. Pray for help and strength, and thank your god.
If you do not believe in a god, then pray to your ancestors or the Earth. You may also choose to pray to your Higher Self, that is, the older and wiser version of you that you will come to be, whether it is the next day or further up the timeline. Give thanks for making it through the day, and pray for help and strength to be able to deal with the next day. Trust that you worries are now in safe hands, and let them go.
Whatever you do, do not stress yourself out trying to find the perfect words, or trying to put together the perfect prayer. Just note that you can actually stop feeling down and out for a second by concentrating on your prayer. Then lay down and relax, and feel how you no longer have to carry the burden alone. Still cannot sleep? Get up and do your prayer again. See what you have missed.
You should repeat this ritual every night until you no longer have to worry or think about it, but there is no need to feel bad about failing to say a prayer once in a while. It is no competition, it is just a tool to help you stop worrying and get some much needed sleep. Your root depends on it. As with everything else: a lot of practice makes it easy. Pray to sleep.