Okay, since it hasn't been mentioned yet: The Badger and Blade
(especially the "ShaveWiki") is a great shaving reference. The tutorials are especially good for starting off with, and the forums are good with an active, helpful community.
I now use a hot towel before each shave (about 1 min., then re-soak and apply for another min.), make my own lather and apply it w/ a badger brush, and use a safety razor. I get a smoother, closer shave that I ever did with cartridges, and the safety razor blades have been good for 5 shaves so far (I haven't pushed beyond that yet), where I would usually kill a two-blade cartridge is just one use (2 uses w/ a Mach). Overall shave time is maybe 5 min. longer than it was with cartridges, now that I've gotten used to my routine.
I use a '58 Gillette Executive that I inherited from my grandfather; a similar Gillette "Fat Boy" tends to be a fairly "gold standard" for used razors among users on the B&B, with Merkur getting a lot of the "new razor" crowd. So far I've only used cheap Personna blades ($4ish for a 10/pack, Walmart), and a puck of Van Der Hagen soap ($2ish, also Walmart), but they've still gotten the job done. A little witch hazel now and then before hand seems to work for an astringent. I've found I get better audio feedback from using a safety razor (you can hear the blade against facial hair more), and the idea of making my shave in "passes" (lather - first pass; with the grain (WTG) - lather - second pass; 90 degree "across" the grain (XTG) - lather (work up a good lather, you'll have plenty for 3 or more applications) - third pass; against the grain (ATG)) seems to make my shave smoother and closer at the end. Each pass works at reduction, with the final ATG pass being the one that takes it down to "baby-rear smooth".
Note: If you are seriously considering going ahead with a safety razor, look at an adjustable. Adjustables vary the "angle of attack" of the blade, so you can have a more "aggressive" angle (I find a 7 on Gillette is "my number"), or dial it back if your skin is more sensitive. You can "start small and work up", as opposed to dropping into a "set" angle of a non-adjustable.
This requires paying more attention to your face (knowing which direction your facial hair grows on each cheek, jawline, chin, neck, etc.), so there's probably a decent amount of benefit from "actually paying attention to what I'm doing" vs. "dragging a razor across my face to get the job done." Some people go on to talk about the "Zen of shaving"; I think it's more about simply slowing down a bit and paying more attention to what I'm doing to get better results...
Take a look at the B&B, check out some tutorials, and see what you think. Some of the basics might help you get more out of your current shave, and you can go on from there...
"Rights of the people that are not exercised on a regular basis, have a bad habit of being taken away from the people."