I started with D&D 4e by listening to the penny arcade podcasts from the start. By the time I was done listening to them all I had a good grasp of the rules and from there I just went online and watched videos of people playing to fill in the rest. Then I skimmed over the books to fill in any gaps I was still missing and learned as I played by DMing back and forth with a friend over skype and roll20.net. Also, listen to the critical hit podcast on the major spoilers site. It's the single best D&D thing going.
Here's my suggested order for learning how to play D&D 4E:
- Penny Arcade Podcasts- Start from the beginning as they explain a lot of the rules at the start as one of the players goes in completely blind. And avoid clicking on each episodes picture art until after you have listened as it spoils stuff that happens in that episode.
- Grab some of the books and start reading them. Plenty of locations online to get your hands on them. Assuming you are evil alignment in real life. *cough* pirate *cough*
- I then suggest grabbing a friend who has done steps one and two and just start playing and dicking around. Make little mini adventures for each other to play and switch on and off being the DM. It seems scary at first, but it's super rewarding and is the best way to learn the game.
- At this point you should have a pretty solid understanding of the game. Congratulations! Now you can argue why edition X is so much better then edition Y and why people who like edition Y are all terrible people.
I suggest just enveloping yourself in all the D&D goodness that is out there on the internet for you to explore and find. The official D&D youtube channel has hours and hours of videos they recorded of the guys who make the game playing it. Some of the later stuff is for 5E, so to avoid confusing yourself I would just stick to the older stuff until you have a solid grasp on the edition you are trying to learn.
I personally suggest going with D&D 4E over other stuff because it's so popular and has been around so long that there is a wealth of resources and information out there that makes learning it much easier then other things. 3.5 has quite a bit as well, but not nearly as much as 4E. I see some Pathfinder stuff as well, but I'm not into it so I can't comment.
Seriously. Listen to The Critical Hit Podcast. It's the best! It starts on episode 8 because they did some test stuff before hand before they committed to making it an ongoing thing. So do't worry about 1-7. Nothing important is in there. It's on their site somewhere, but I can't remember where. It's in some weird corner if you want to poke around and hunt for it.