You would have to explain what exactly each table/field mean (the concept of category/forum seems to be different).
I also suggest you to create the categories and forums through ACP, as Dick said.
Importing users must be easy. Read the data from your old db, put it in an associative array and call user_add() (the phpbb function). The keys of the associative array is the name of phpbb users table fields.
Mandatory fields are: username, group_id, user_email and user_type. You can pass group_id and user_type as constants: 2 (registered users group) and 0 (normal users), respectively.
But you can import much more info, have a look at the wiki to see the fields of the users table: http://wiki.phpbb.com/display/DEV/Table.phpbb+users
The topics and posts may be directly inserted in the respective tables, but calling submit_post() has the advantage of synchronize everything by itself.