If your keeping the old server you can setup the new install to point to the old database. If you are not keeping the old server then you would want to export your database on the old server and import it into the new.
If you have command line access on the old server to export it you would do something like:
mysqldump -u YourUsername -p YourDatabase_name > osticket.sql
Then on the new server you would do something like:
mysql -u YourUsername -p YourDatabase_name < osticket.sql
If you have access to phpMyAdmin on either host it has its own import/export options which make it pretty trivial.
