This should be really easy.

Download Bromine from http://bromine.openqa.org/download.jsp

unpack and copy all files to a folder named Bromine on your server

Now open yourservername/Bromine/install.php in a browser.

Fill in the forms:
Username: Name of mysql user
Database: Name of database to hold the Bromine tables
Password: Password for the mysql user
Host: Usually 'localhost'

And press 'Install'

You should get a message saying 'Install complete'

Now go to yourservername/Bromine

It will tell you to delete install.php and sql.sql, so go ahead and do so

Now reload yourservername/Bromine

You should see a blue login form. Login with username: 'admin' and password: 'admin'
Now go to the admin module -> edit users and change your users to something a bit more secure.

All done. Any problems? Post them in the forums

You can also get the newest bleeding edge Bromine revision with SVN. Grab the files from https://svn.openqa.org/svn/bromine/trunk with something like http://tortoisesvn.tigris.org/. Follow the same procedure as above, but run patcher.php before trying to log in.