Since I'm going to be teaching teenagers soon, I'm assuming I'll be covering a lot of basic things. The following are a few rules of thumb for mixing (I'll say that again: RULES OF FUCKING THUMB). They are very simple, but they are good tips and a lot of people don't know this stuff.
Kick Drums: Most people think that kick drums are supposed to be chocked full of low end. Sadly, even being 3 weeks away from graduation, I still see one or two people in my class that take any and every kick drum, then crank up a low shelf EQ on everything below 100Hz. I don't know why, because it's been beaten into us over and over and over that you shouldn't do that. The truth is that kick drums sound muddy as hell if you do that. If a kick is recorded right, you really shouldn't have to add too much low end. A good trick is to boost somewhere up around 4K-6K. Just use a parametric EQ and sweep the high end until you find the solid thwacking of the beater hitting the kick. And when you are adding low end, don't rely on the low shelf. You can use it a little if you want, but you should really search for the clearest frequency in the bottom end.
Bass guitars: The same goes for basses. Don't just boost the low end. Try to boost some highs until the bass sounds really clear and you can actually hear the picking sound against the strings. This will make it easier to tell what the hell the bass is doing. If you boost nothing but the extreme lows, you end up getting a "one note bass" and you can't even tell what it's playing. Also, take a look at a Chart of Equal Temperament, and find the frequencies that correspond to what the bass is playing. This really helps when there is a dip in the bass at a certain note. You can then use the chart, find the frequency, and boost it with a narrow Q until it is level with all the other notes.
Mixing Basses and Kicks: A lot of people just boost lows on both kicks and basses, and they even boost around the same frequencies. Try to make sure that one is on top of the other. You should find which one is the best foundation. In almost every case, I find that the bass is the best foundation, so I try to make sure to boost the kick at higher frequencies than the bass. That makes the kick really stand out instead of trying to leave the kick and bass on the same plane and fighting against one another. That just results in mud.
Heavy Guitars: Everyone knows that it feels awesome to play an electric guitar and have all that sweet low end during your "chugga-chugga-chugs", but having too much low end results in mud because your guitar is now fighting with the bass. A lot of engineers use a low cut on all guitars. Personally, I cut everything below 75Hz, and attenuate everything else below 100Hz, but just a little. Also, guitars can be tough because they sit right up there around 1K-4K with vocals. Try your best to avoid boosting the guitars in areas that fight with vocals. Every situation is different, but boosting a little around 1.5K and cutting a little around 600Hz helps. I emphasize the word AROUND!!! Don't aim specifically at those frequencies. It's not the same every time.
Panning: Panning really depends on personal taste, but if you're panning a bunch of background vocals, it helps to make sure none of them are sitting on top of one another. Say there are 6 background vocals with pairs of different harmonies. Well, throwing the highest harmony out around 40, then the middle around 30, and the lowest around 20 (and the same on the other side: -40, -30, -20) really helps clear things up and make the vocals sound huge. And again, I said AROUND! Plus, it doesn't make sense for them to all be sitting on top of one another. If it's supposed to be a bunch of people singing, why would all of their heads be in the same place?
More panning: I usually throw heavy guitars all the way hard left and hard right. I was always afraid to do this in the past, but Scott showed this to us once, it sounded freakin great, and I've been doing it ever since. Sure, I'll put some more guitars further toward the center, but my main rhythm guitars are always hard left and right. For lighter guitar tones or acoustic guitars, it's "better" not to put them out so far, but I won't lie, I still put a ton of my clean guitars all the way out. I also do the Butch Vig thing and put a darker-toned guitar in the center, but very low. I find that it works because it fills in the gap, makes the bass feel less "naked", and it doesn't fight the vocals as long as it is dark and very low. I do it in a way that makes it unnoticeable until you mute it. Once you mute it, the track sounds empty and you're dying to put it back.
Panning drums: I heard a great trick and I've been using it all the time. Listen to your overheads, then pan your drums according to how they fall in the stereo image of the overheads. It makes everything really tight. The only thing I ignore is the snare. I always put the snare dead center, and so does just about everyone else in the world. I'm not going to go further than that, because there's this huge argument over whether or not you should pan them in drummer's perspective (hat left, ride right) or audience perspective (hat right, ride left). But I will say that I do drummer's perspective, and it kills me to do it the other way.
....Ok, that was a lot, so I'm gonna stop now.
But as I said before, these are rules of thumb, not strict rules. It's best to do whatever sounds good to you. These are just good starting places if you are having problems. And please don't be the kind of douche that just does this stuff without really listening to see if it needs to be done. I've had assholes come in and listen to my mixes, then I ask them what they would change, and they immediately say, "Well you should bring out the high end of the bass because blah blah blah, and you should bring out the high end of the kick because the kick isn't really a 'bass instrument' and blah blah blah, and cut those guitars at 500 and don't pan those toms out so far because that's not where they are and blah blah blah I'm a huge douchebag dickface." Little did they know that I had already done those very fucking things, and to extreme extent in some cases. Needless to say, I stopped asking those people for their opinions and now view them as total dumbasses.
Don't be that person. If you become that person, then I really don't like you. Listen to something, decide what you think should be done, try it (or if it's someone else's mix, ASK IF THEY'VE TRIED IT), and see if it actually works.