To put a style on your forum, you dont need to register there. You can simply click browse styles>pick a topic and style that you like.
On YOUR forum, go to admin>manage styles>create, then create a random style and save it. Then do admin>manage styles>edit, and choose your style to edit. Scroll down to its CSS code and delete it.
Go back to styleyourforum, and on the style you wanted, scroll down to its CSS code at the bottom. Copy that code and place it inside your CSS code for your forum.
You could also follow this guide
http://www.smfsupport.com/support/stylesheet-codes/how-to-install-a-stylesheet/-------------------------------------------------------------------------------------------------------------------------------------------------------------
EDIT: i think i realize you want to register to add your style to the website. If so then you should be able to register. Can you tell us what happens if you press register. You said nothing happens?