I used to develop for Android and iOS, and for multiple screen support we use to use mdpi, hdpi, xhdpi.
Now I want to develop for Windows Phone, I want to set a background to a button and I don't know how to define image size to support all screen sizes.
You dont need to provide different assets. See info from MSDN below. There is a way to support different assets/resources. But we have never done this bevore in our apps.
From MSDN:
Assets such as graphics, video, audio, and icons make up a large percentage of an app’s size. Including assets for all resolutions in your app uses a lot of space in your app. For most apps, we recommend that you include only WXGA assets. WXGA assets have the highest quality, and they automatically scale to work well for other resolutions.
More info: Multi-resolution apps for Windows Phone 8