Watch the first season through. You'll miss/not understand 2/3 of what's going on (it IS complicated, but that's what makes it fantastic - it's an adventure story with layers of history and politics and schemes). Once you've watched the whole first season, start over, and this time through a TON more will make sense - you'll understand who the people are and why they're doing that they're doing.
That's one of the great things about the show (and the books): there are so many layers that you get enjoyment and learn new things with multiple readings/viewings.
Honestly I usually watch each episode 2 to 3 times the first 24 hrs it comes out. Watch season one, watch history and lore season one, game of thrones wiki. Proceed like that. Once you get into it you will know which information and storylines you want to know more of. Then wiki, YouTube etc. At this point you will be hooked so enjoy. Deepest most complex character stories ever created in an epic fantasy world. Pretty freaking amazing I have watched all five seasons this week
There's a Game of Thrones wiki and several other resources you can use to help you better understand the story and characters. Just make sure you study the show and not the books, There are several differences.
How many seasons has it been running for? And do they re-run episodes? If so, you can use your DVR, configured to record all episodes and keep them until the disk is full. Terminology varies with different carriers, but you'll get them all eventually. Or see is season box sets are available if you can't wait.