I have insomnia and take prescription sleeping meds so I'm not too sure how the various methods I tried before sleeping pills would work on you.
A while back I followed breathing therapy with my physiologist to help recover my lungs from a surgery. It's very relaxing, kind of like meditation.
You can do it at home without any assistance of course, I taught it to my mom and she sleeps in quite a bit faster and it has also reduced her snoring significantly. I can't explain the whole regime in text but I'm sure you can find a good amount of information about breathing therapy online and see how it works for your sleep.
If you have a severe sleeping issue, I'd advise you to try literally every natural form of sleep aids before even thinking about prescription meds.
Melatonin is pretty effective in helping people with mild sleeping in issues. It is a natural hormone that your body releases when the body thinks it's time to go to sleep. You can buy melatonin tablets from 1 to 3mg freely without any prescription and take them when you're about to go to sleep.
Melatonin is commonly used for jet lag, because it can make your body think that it's time to sleep regardless of when you take it, giving you some degree of influence over your circadian rhythm. This makes it very useful in getting back to a consistent sleeping schedule if it has been irregular.
If various forms of relaxation/meditation techniques don't work, I would advise reading a book or melatonin and see how that helps you sleep in
