Hi,
You have at least 3 choices:
1. Install MySQL DB server on client's computer
2. Install MySQL DB server on client's computer located within his Local Area Network
3. Use MySQL DB server installed on external hosting and connect via internet
Chosing first or second option is good if your app will be used by one or more users on LAN without access from internet.
Third option is good if you are planning to connect to database over internet from different offices not located within one network.
IMO best option to deploy database is by creating install scripts and generate database from that script while installing your app or on app's first run. As far as I know you can use MySQL Workbench application to generate that script (link below) or PHPMyAdmin.
Link:
http://dev.mysql.com/doc/workbench/en/index.html[
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[Update for a comment]
It depends on how you know how to connect to MySQL server. If you provided connection info (host/dbname/user/pass) inside your code you will have to modify your application. You can add configuration window to allow user enter connection configuration and then store it in configuration file. On app startup read that file and dynamically build you database connection string. If configuration file is missing or connection info is not present in that file you can display DB configuration window and not let user run your app until he provide necessery data. Remember to encrypt DB password in configuration file!
I hope it help you.