In general you need to create server API: choose some format to talk to between your web service and android application.
Then you'll always be need to request some data from server, that will be returned to you in format described above in a body of network response of some sort.
Next all you need is parse this data and populate to your adapters or whatever.
Note that networking operation might take quite some time depending on your connection, so you can't wait while it ends to show your UI - you need to do this in async manner, and give user a feedback that data is retrieving.
Nowadays json format passed in body of http post requests are quite popular. Take a look at this tutorial on how to parse json on android and this video about how to create json api in php.
Of course you can try to connect to remote MySQL server directly.. It really is more simple solution in some cases (you don't need to code server-side api), but might be not so accessible because standard MySQL ports aren't opened in all networks. Also your API server might hide some implementation details on how is data stored in reality, thus allowing you to migrate for example from MySQL to PostgreSQL without pain for android application.
Don't forget to secure your data from unauthorized access!
EDIT
It's 2017 and what would be the easiest option now is to use opensource project which will provide rest api for your database, for instance ArrestDB or postgrest