Stress hormones take time to leave your body, and they keep you awake. When you are frustrated that you can't sleep, that creates stress, which makes it harder to sleep. When you think about your stress of the day it creates stress too.
One big thing is to keep away from caffeine. Caffeine works essentially by slowing the rate that stress hormones dissipate.
You can't really do too much to speed up that process, so the best thing is to stop building more stress. If you have difficulty sleeping, stop trying after 15 minutes and take a break. Do something not very exciting or engaging. Then try again. Similarly do something that stops you thinking about your hard day, for me that's really easy to shut off and takes practice, but for you just try to find something that works, meditation, reading a book, writing, drawing, walking. Just avoid things that are going to build adrenaline like strenuous exercise or competitive video games.
The goal of the previous is to reduce the factors that keep you wakeful. The other side of the coin is that you can increase the state that makes you seek sleep.
Seek satisfactions. Take stock of your body, are you hungry? are you sore? are you dehydrated? do you need to go to the bathroom? Correct these things. They're easy, but you'll make yourself that much more comfortable, and at the same time you'll lower stress.
Take stock of your mind. What is your mind craving? Do you want stimulation? Do you want entertainment? Do you want to socialize? Do you want to relax? When you can, do these things.
This is going to make you feel satisfied.
Sleep crudely works in that there are some hormones that keep you awake, and some hormones that make you want to sleep. Wakeful factors are generally stress-related hormones, which are one of the things that we have most control over increasing, (it's easy to work ourselves up) but hard to decrease (they have a half life in our bodies and can't really be forcibly purged). Then there are restful factors that are generally satisfaction related, seratonin which is crudely a 'things are good' kind of chemical turns into melatonin which is crudely a sleeping factor. Others build up during the day.
Sleep happens when your pressure to sleep overcomes the stress that keeps you awake. I think that keeping that in mind lets you stay healthy.
I think there's a few things we can do in a pinch to help directly too though, but relying on these mean that there's something wrong that you're failing to correct. For instance, a bit of alcohol can be a great way to break the cycle of stress worrying about the day. This can allow your stress levels to drop and even after it's out of your system, you're out of that cycle of worrying. That might get you some better sleep and then you might have a less stressful day the next day.
Similarly, you could take something like melatonin, but again that's artificially taking the place of a feeling of satisfaction and accomplishment. Again, if it's an occasional thing it might be helpful, but if it's covering for the fact that you're always working overly long in an unsatisfying environment and not getting time to yourself, it might be worth it to identify it and work to correct that issue.
That said, everyone's different, and everyone's bodies and brains handle things differently. For some people they might just not properly respond to a normal amount of sleep pressure and have insomnia. For them taking supplements might not indicate anything wrong with their environment, it might just be a quirk of their own personal condition.
But I think we should always look at ourselves first. Not because I'm against supplements, but because it's good to know if our bodies are telling us something. I don't have trouble sleeping, if I go through the process of trying to determine what I'm missing. Whether I'm craving some creative stimulation, or some mindless entertainment or whatever. But generally when I commit to bed I'm asleep within 15 minutes. However, sometimes I realize that there are some things that I need to do to be satisfied that are going to keep me up late. If I had a hard day, I know I'm going to need more time to recover from it, and trying to force myself to go to bed early is just going to make things worse.