If you live inside the Seattle Market:
Buying local cable or satellite packages is the most obvious answer. Beyond that, it is difficult to watch Mariner games. That's tough news for those of us, author included, who have no desire to pay for cable because Mariner games are all they watch on that spectrum. In that case, you have a few remaining options, none of them particularly fantastic.
You can always watch at a bar or friend's place but that's pretty hard to do consistently. The option I personally went with is buying a slingbox and hooking it up at a place that has a satellite package. This allows me to tap into and watch that TV from anywhere with an internet connection. Unfortunately, it comes with a noticeable 2-3 second delay from all the routing.
If neither of those work for you, there are slightly more illicit options that I will acknowledge the existence of, but not go into too much detail about. That information is readily available with a bit of internet sleuthing. Non-authorized web streams of sporting events are out there. Also, websites determine which market you are in based on your IP address. There are ways (e.g. VPNs, proxy services) to spoof your own IP to make it seem like you are connecting from somewhere else.
If you live outside the Seattle Market:
MLB.tv is a great option. It's pretty wonderful and not that costly when you consider all the benefits it comes with. It's certainly a lot cheaper than cable packages. If you already have cable/satellite, you might also consider MLB Extra Innings which is baseball's equivalent to the NFL's Sunday Ticket. When it is more affordable and more attractive to follow baseball from outside the market you live in than within in, the system has some messed up priorities.
If you live inside the Seattle Market: 710am. Get a radio; it costs like $5.
If you live anywhere: MLB Gameday Audio costs $20 for the entire season and comes with no blackouts. There's also the MLB At Bat mobile application which comes with access to MLB Gameday Audio and some other features and is $15
There's MLB.com where you can load up Gameday for each game. Each of the major players in the internet sports world (ESPN, Yahoo Sports, Sportsline, etc) will have their own version of a gameday as well. I highly suggest that if you are participating in a Lookout Landing game thread that you have at least one of these open in another tab/window. That way, you can avoid having to ask questions like how many pitches so-or-so has thrown.
Seriously, it's annoying. That information is just a mouse click away! If you have further questions or want more detail on something (e.g. "how far was Cust's HR in the third?", "How did Felix's command look?"), feel free to ask, but don't enter the game thread in the 7th and want to be filled in on how the runs scored.