I'm playing on the mac and the replay browser won't even record any of my recent games. Do I need to activate it or something?
To watch replays, you should head into your Match History after playing a game, and in the bottom right corner it should say "Watch Replay".
Once you click that, it'll open the Replay for you, and you can enjoy it. It's pretty buggy right now as its still in Alpha, so be prepared for that. Once your replay exits (whether you close it, or it was finished) your client may or may not have a black screen (a known bug). If it does, restart your client, it should be alright. If it's okay, then that replay you just watched will now be in your "Replay Browser" in the top right of your lobby (it's the icon 3 to the right of the Riot Store). It'll be stored there on your computer after you've watched it once from your Match History.
I hope this helps. If you still can't seem to watch replays, let me know, maybe they aren't available to MAC right now, though I think they should be.