The one advantage of machines over free weights is that the machine will enforce your form. If you are able to maintain form with free weights, the effort exerted to do so is an added bonus, but if you aren't, it's not good. I started with machines, and every couple workouts replaced a machine exercise with a free weight exercise. This helped me get started, and let me concentrate on the form on one new exercise at a time.
The best way to learn a free weight exercise is to simply start doing it without any weight. Start squatting and dead lifting with just your body weight (use a broom handle to simulate the bar). Once you get that down start adding weight. There is a very little that a machine will do to help you with exercises like that and in fact it could end up enforcing bad habits.
TAKE VIDEOS. If you're hesitant to bring a point and shoot to the gym, go later at night or before noon when the gym is relatively empty. Share your videos on any of the big lifting forums and ask for opinions. Sure, you can ask a trainer, but if you're lifting at any of the major chain gyms I wouldn't trust a lot of those guys to critique a squat as far as I can throw them.
If you're doing a lift with improper form, you might as well not do it at all. The point of maintaining proper form is to not only remain injury free, but to also point out any strength imbalances you might have (weak quads in a deadlift, weak lower lumbar in a squat, etc etc).
(example vid, i switched to sumo-stance for deadlifts and wanted to make sure i was doing it right before moving back up in weight -- http://www.imperial.org/~jd/deads275.wmv )
I can respect -anybody- that posts videos and asks for help on form. The amount of weight you're moving is trivial - the fact that you want to focus on your form and perform the lift correctly speaks volumes. I respect the guy squatting 95lbs correctly infinitely more than the guy squatting 405lbs to 25% depth any day of the week.
Luckily I haven't had to post and vids because I have a trainer friend who is very good at form and correction. He just adjusted a few things in my DLs and I'm closing in on 500lb DL again.
I've tried sumos off and on, but I don't they are right for my body type. I have long arms and legs and I just get so much more leverage with the traditional DL. I do sumo holds though as accessory work to keep my glutes firing properly.
And yea, the guy quarter squatting is generally a dumb ass. There are times to quarter squat, but for most people they should never need to.
Good form is vital though, so get 'Starting Strength' by Mark Rippetoe. There are plenty of exercise books available, but this is the only one I know of which will spend 50 pages explaining the proper form for the squat. There's even a companion video for the book.
It doesn't they very much about programming (i.e. how to and how much to increase the weights you lift), but you can get advise on these from other sources.
Of course, I'm 48, and when I was 18 I would have laughed at what I just said, because I was powerlifting. But my needs are different now. I do 30 minutes of interval training cardio, and 20 (or so) minutes of weights. I do 2 (maybe 3) sets. The first one is about 12 reps, where I do 4 warm-up reps, 4 at medium weight, at 4 at just-below-what-I'm-lifting-that-day weight (depends where I am in my cycle). I need machines to be able to change the weight "on the fly." Then I do a second set to failure (again, how many reps depends on how much weight I am pushing that week). This quick routine gives me the workout that I am looking for at this point, and I can get it done in the time I am willing to commit (4 days/week).
If you don't know what I mean by "where I am in my cycle" (I'm male so it's not that) check out this link:
http://www.deepsquatter.com/strength/archives/tomdesign.html
The only problem is I may be running out of weight on some of the machines. I'll deal with that problem when I get there, though. The more likely result is that I'll lay off the weightlifting for a while and have to "rebuild" before that happens (if, say, I start sailing alot).
Edit: typos
Free weights can be more forgiving when your form is a bit off (versus being locked into a groove that leads to a pull or tear).
"A kid walked up to me in the gym while I was dead lifting and asked 'what muscle does that work.' I responded by asking the kid 'have you ever watched a football player run across the field and tackle the player with the ball?' The kid responded 'sure.' To that I said 'that muscle.'"