When you access your mysql server on Yahoo business plan, you have to create a new root user. This username and password can be different from Web Hosting user name and password.
1) Visit
http://smallbusiness.yahoo.com/services and type your Yahoo ID and password.
2) Goto: "Web hosting control Panel"
3) Choose "create and update"
4) scroll down and select "Mysql database".
5) Click on "Database Administrator". If you are accessing mysql for the first time and no root user exist, then you will have to create one.
6) Now click on "Install admin tool" to install phpMyAdmin.
7) You will have to click on "I agree to terms and conditions" and then choose the directory in which you want to install the software.
8) Now access the phpMyAdmin from IE or firefox browser by going to that directory where you installed it. for eg. yoursite.com/myadmin
9) Type your username and password (The one you created in the step 5 above and NOT the web hosting username and password)
To access the database from a php page, use "mysql" as your server (instead of usual "localhost") along with the username and password created in the step 5.
Note: Yahoo does not allow remote access for security reasons. So any desktop software that you may try will probably won't work. You have to upload the php or perl pages to your server and acess mysql database from within those pages (for e.g. phpMyAdmin). An unfortunate shortcoming of using Yahoo web hosting!
Disclaimer: I am not an yahoo employee nor have any shares. I am using Yahoo web hosting for last 1 year and I am happy with it.
I hope this helps.