Well, one way you can start is to break it up depending on how messy it is. So like if there are shirts that need to be folded, do that on the first day, or maybe you can even do two things like the pants to fold. Then the next day can be hanging clothing. You can also make cleaning more fun by listening to music! If there are items that belong to you, take them all down and look through them. If there are some things that have no use, throw it away. For me it’s kind of hard to do that but I understand that it’s a great way to tidy up.
I think you should find yourself a time period in a day were you're completely free to empty your closet completely, see if there are some things you want to get rid of, and re-organize. Instead of looking at the mess, clean up. Look at videos on how you can fold better to optimize space if you need it! But trust me. It's only by re-organizing that you will clean up better.
You could try to do just a little every morning when you wake up. Then it will get better after a while. Or you could try to make time at weekends to clean it.