How do you Color Correct?

If I'm feeling lazy and I like how I shot it I usually just use a combination of premier's built in tools, curves, quick correct, etc. For more important stuff speedgrade can be nice, honestly though, I don't do much in the way of coloring.

If it's anything seriously in-depth, I prefer DaVinci Resolve. You can transfer your timeline perfectly from Premiere to Resolve with an XML (with a few exceptions like position and scaling and some keyframes), and Resolve Lite is free. I feel like all I do on M&A is talk about Resolve, but I really like it.
For everything else that just needs a quick, decent color pass, Colorista rocks. I've never had a successful time with Speedgrade.

Inb4 Color Correction vs. Color Grading

But seriously, if everything is done correctly in camera there's not much you need to do in ways of color correction. I personally use Premiere's 3-way color tool and adjust levels and saturation for 90% of my footage. If something is really screwy i.e. gnarly color cast then I'll run it through After Effects. Other programs and plug-ins are overkill for most situations.

I prefer RED Giant's Magic Bullet Looks for the more detailed color grading. If not, the three-way color corrector is gr8 m8 ; = )

I correct and grade on Resolve and have used most programs available at this point. The important thing is to shoot to the strengths of your setup (i.e. knowing if it's better to over or under expose your specific camera in a tough situation) and having a proper way of viewing your footage. It's hard to explain to someone that the most important tool for correcting is the monitor itself; if you don't know what you're really looking at (and unless you can read scopes and waveforms like the matrix) you're shooting yourself in the foot.

Learning on speedgrade is a good way to go though. Avoid relying on pre-built look effects like magic bullet looks, it can get out of control quickly.