Some host will do this for you for free. You can do it easy too: Archive, zip, your full database if it’s larger (or if small just download it as in .sql file.) Archive all your files and folders into a zip file. Download the 2 zip files. Create the same database on your new host (same password, dat name, dat user) and reinstall then from your donwloaded one. Upload the other zipped files to your new host into a www directory where they belong, extract them there. You can preview your website from cpanel (or plesk panel it depends what control panel you have).
Then configure your DNS pointing it to your new installation space (you will get all the IP etc. from your new host or they will do it for you if you carry also your domain name to them.)
