Apple TV will allow you to watch some games for free, but not all.
As Day2 mentioned, you can get the Season Pass for free via T-Mobile if you have T-Mobile or know anyone that has it. The Season Pass can be shared with up to 6 other people, so for example, my parents, myself, and my friend are all sharing the Season Pass between our 3 Apple TV accounts.
It's a pretty sweet deal, especially with the much improved presentation of the games. It was difficult to watch DC games locally the past few years and when I was able to watch, it generally looked like crap (in addition to the team being bad lol). It all looks great now.