There's no short way of doing this unfortunately. I'd suggest going through the
installation process. From there, open up PhpMyAdmin (or whatever database management tool you use), delete all existing tables and then upload your database from icyboards. This is where it may start to get a little confusing...
Now you have MyBB installed you're half-way through the process. In your files, go to inc/config.php and update the database prefix to the one that should now be in PhpMyAdmin. An example of your prefix should look something like this when looking at your tables:
*_users
* being the prefix, and "users" being the table name in the example. Last step... Now go to your settings table and update the following:
- Board URL (bburl) - Should be the link to your forum and should not containing a trailing slash. For example, http://domain.com
- Homepage URL (homeurl) - Link to your forum.
- Cookie Domain (cookiedomain) - Should be .domain.com be sure to include the dot (.) at the start
- Cookie Path (cookiepath) - Should be just a slash (/). If your forums in a sub-folder, it'll be /subfolder/
Hope this helps.