I have a MySql database with some sports results in it. I want to write an Android application to display these data on mobile phones.
I´ve searched on the internet
You may want to look at C2DM (http://code.google.com/android/c2dm/).
A common way is to write a REST web service and have Android call that and get the data from the server.
If you want to push it, if the data is small enough, you could use SMS and just send the data as a text message to the device.
You don't want to open access to your database so by using the web service you can better protect your database.