I am looking into using mysql and php. I bought a book which is fairly good but is not so clear on the instalation. I have mysql and php installed on my server, but in order to create a database I have to pay my host a small amount of money. Do I still need to install mysql on my computer to edit the mysql database and then publish it to the server to use this database and if php is installed on the server do I just publish the files to the server to test them?

Any help would be apreatiated.

to use the remote database on your host you do not need MySQL on your local machine. you just use your hosting server for testing.

Or you can setup a webserver, PHP and MySQL on your machine and use that for learning on.