Some general tips:
- Shoot more. Especially people, if that's what you want to really improve on.
- If you haven't got it already, get a copy of Understanding Exposure
by Bryan Peterson. Learn the exposure triangle - how shutter speed, aperture, and ISO work together, and how to choose the settings to make a good photo.
- Join the forum on http://www.photography-on-the.net
- Shoot more. Practice makes perfect.
- Evaluate and study other photos that you like and want to emulate. Look at the lighting, the posing, the framing/composition, the background, the colors, the processing. Evaluate other photos that you don't think are very good, for the same reasons.
- Shoot more.
- Work on your processing almost as much as you work on your shooting. Find a good raw processor and organizer like Lightroom or Aperture, or even the DPP raw processor that came with the camera - and learn how to use it, either by online training, or by in-the-flesh classes. Proper processing can take a photo from "pretty good" to "WOW."
- Don't obsess over gear, but also don't be afraid to pick up a few extra items. For a beginner, the two things that I would recommend to complement the T2i are the 50mm f/1.8 lens (colloquially called the "nifty fifty"), an external hotshoe flash such as the 430EXII, and maybe a cable to take the flash off the camera.
Pick one or two photos and I'll be happy to give a critique when I can see them. I can't get to DA or Facebook from this computer right now.