Currently my gear isn't good enough to get into herioc queues yet. I've been running regulars to try and get some gear and surfing the AH for crafted items, but I haven't even come close to the 329 (or whatever) item level I need to queue.
I really did not use justice points to buy anything but my off hand weapon. i regret that because it took me waaaay to long to gear up for heroics. so use justice points and just run randoms, run with a tank you know well to speed up the process, get in vent and start up a convo to make it more enjoyable. also, look at your gear, what items are below ilevel 333? look up on atlasloot some items you can replace the old green and blue gear with and run the dungeons that drop them. you should be geared for heroics in no time.