There are few ways to do this. I suppose you have shared hosting package on that installation and that you “only” need to change your domain name.
So one solution would be to rename your hosting package to another domain. If your domain is now somedomain.com, and you want to transfer it to someotherdomain.com, you will rename your hosting package to it and point DNS for someotherdomain.com to this server where the files are located. Also you will need to change in wp settings WordPress adress(URL) and Site Adress(URL). You change that also to link of your new someotherdomain.com. And that should be it in up to 48h when DNS do what it needs to do(usually faster).
The one minor problem with this kind of just “renaming” is that if you have a lot of media links (images, videos, etc) you will need to (in most cases) manually change it to new links.
To avoid that you can use (what I use, even if I just changing domain name) plugin called DUPLICATOR. So if you have shared hosting you can open new package for this domain and just tranfer files with duplicator and in this case the links will be automatically changed(I would recommend this for larger sites with much of media links etc), and also all the database links.
I hope this helps.
Regards