I'm not familiar with A ticket. The basics would be:
1. back up your database.
2. Create the OST database and username/passwd with permissions.
3. Follow the normal steps for setting up OST.
4. become intimate with the two table structures.
5. write a few monster SQL queries to move the data from database1.tableA to insert it into ost_db. Do not expect data to be stored the same way. Or a few relatively simple scripts that will grab the data, loop through, and insert the data.
6. back up the new database before each volatile query.
Repeat until done.
in the aticket packed the install/create.sql file and the osticket setup/inc/osticket-v1.6.sql both contain the original SQL setup commands. It should help reduce the amount of time that you would need to craft your queries.
example:
INSERT INTO TABLE2 (COL1, COL2, COL3) SELECT COL1, COL4, COL7 FROM TABLE1
