The Android Operating System is designed so that you have several ways to configure your background, or wallpaper. There are a tremendous amount of images available online which you can use as your background.
Android devices come in many flavors, developed by many different manufacturers. So you can imagine that the resolutions can vary quite a bit from device to device. Fortunately they haven't made things too hard for us. You will find that the resolutions are about the same for each generation of devices released. The so-called first generation devices, such as the HTC Dream or the HTC Tattoo, which would be the devices running on Android 1.5 and 1.6, had smaller resolutions, such as 240x320. The second generation improved on this significantly, bringing resolution sizes up to 480x800. The third generation, including devices such as the HTC Evo 3D, went a little further bringing the resolution up to 540x960. Keep in mind that each generation of these devices aren't necessarily the same, you will need to look it up to verify. Simply doing a Google search for the name of your device plus screen resolution should quickly give you your answer.
Many people will become confused as to what image resolution they should be searching for their particular device. Especially when you know that your device has a resolution of 480x800, but when you search wallpapers for your phone online, all results show images at 960x800. What is all this about? Well, in case you haven't noticed, android phones come with multiple home screens, which you can switch by simply swiping your finger to the left or right. You will also notice that the background scrolls as you switch home screens. It doesn't scroll the whole width of your screen, but just a little. Android phones dedicate twice the amount of pixels as the screen width to the scrollable home screen. This doesn't necessarily mean that your background image has to be twice the resolution of your screen width, but it can be up to that much, and will looks its best at that resolution.
So how do you get an image to fit your phone? One way could to simply do a search for images in Google along with the resolution of your device. Then you can simply right click the image, chose "save image as", and save it somewhere on your computer. Now all you have to do is connect your device to your computer via USB cable, and copy the image over to your device's SD card.
But wait, there is an even easier way to do this as long as you have a decent internet connection on your device. Just do a search on the web for images, touch and hold the image, then select "Set Image as Wallpaper." Many times you will be asked to resize the image to fit the phone just in case its not exactly the same. For that reason, you do not necessarily need to put too much stock into worrying what size screen you have.
If you really want to make this process easier, find a site that offers free wallpapers designed specifically for your device. Many have the option to find the wallpaper you want and send it directly to your phone.