I’m afraid that’s too broad as a question for us to give you a useful answer. There are books written on the topic and consultants who make their living doing what you ask. There is a lot of reading material for you in the knowledge base https://help.dreamhost.com, too. There are guides there on how to transfer a domain, how to copy files using sftp, setup a database, migrate WordPress-based sites and more.
So, if you want to help on a public forum, please spend more time describing exactly what your site looks like, what technology does it use, where is it hosted currently, how you manage it there… basically, share with others on this forum what you are trying to do in details because there are plenty of books that will answer your very wide question.