Recently we had a project where the client was requesting us to transfer his domain. Hmm I thought it is pretty simple, of course it is as long as you are okay with DB import export etc.
I have listed out steps here:
1) Make a back up of everything including DB
2) Go to control panel and then to PHPmyadmin (if it is shared server, contact your hosting company)
3) Export the DB into SQL format
4) Open the SQL file using any editor.
5) Find and Replace, www.olddomain.com to www.newdomain.com
6) Delete all existing tables in the dB
7) Export the SQL script
8) Transfer the complete source files to new domain
9) Your website should work now
10) You should have used blog site url function to get the url, theme path, image path etc.
I hope this helps up to an extent