Ok, this is certainly outside of the typical use case scenario, BUT it is very doable within Rails and ActiveRecord.
First of all, you're going to want to execute some SQL directly, which is fine, but you'll also have to take extra care if you're using user input to determine the name of the new database for instance, and do your own escaping. (Or use one of ActiveRecord's lower-level escaping methods that we normally don't worry about.) The basic idea though is something like:
create_sql = <<SQL
CREATE TABLE foo ...
SQL
ActiveRecord::Base.connection.execute(create_sql)
Although now that I look at ActiveRecord::ConnectionAdapters::Mysql2Adapter, there's a #create method that might help you.
The next step is actually doing different things in the context of different databases. The key there is ActiveRecord::Base.establish_connection. Using that, and passing in the params for the database you just created, you should be able to do what you need to for that particular db. If the db's weren't being created dynamically, I'd put that line at the top of a standard ActiveRecord model so that that model would always connect to that db instead of the main one. If you want to use the same class, and connect it to different db's (one at a time of course), you would probably remove_connection before calling establish_connection to the next one.
I hope this points you in the right direction. Good luck!