I've been instructing for the past 3 years now, and been driving at the track since 2003. By that I mean, I was going at least once every two months, some months 2-3 times before instructing.
Since instructing, I've only gotten faster in my own seat time, as sitting side seat you take yourself out of the driving equation and are able to really dial in on how to negotiate a series of apexes. You're more able to really dissect the track layout and nit pick at little things and you'll be surprised by how you instinctively start to notice your own deficiencies and fix them. Sometimes you even learn along with/be taught by a student, as their "mistakes" and difference of line can sometimes open your eyes to little nuances that work better.
I get a HUGE amount of enjoyment from seeing the students really start to put a lap together. So much so, that I may go a whole day without even driving my own car more than a few laps (sometimes not at all) for confirmation, or student ride alongs. On those occasions I'm ecstatic at their progress, and start to nerd out and clap and cheer them along when I can see and feel them hone in on what they're doing and having a blast.
Granted I don't have a blast with every student, and sometimes you have to really adapt your teaching style to accommodate different learning styles.
There are moments when it really seems they just aren't grasping what you're asking them to do, and when you have a communication breakdown it's your job as their instructor to figure out HOW to instruct them so they aren't frustrated with the experience. Remember to be patient, and when they don't get it verbally, ask them if they learn better visually. Then you can either show them (you drive their car, or yours), or in some cases guide them with a pre-warned/pre-discussed friendly hand on the wheel.
Also there may be times when you just can't get through to them and/or you're not feeling it.
I've had a few students with no concept of smoothness have me puke my guts out, and some that were pretty close. In those instances, I always find a fellow instructor to swap students with, and generally a change up is all that's needed.
Bring some dramamine with your just in case.
A communication system is a good thing to have as it will definitely save your voice at times and make the whole experience much more relaxed. I don't have one right now, so I'm reduced to raising my voice.
For safety, the main thing is to trust your instincts. Don't take their signed tech sheet as gospel and do your own assessment. Walk around the car and take a look at tire condition, and other parts, and take the time while sitting on the grid to talk to the student about the car and what they've done/how they maintain it.
If you don't feel 100% safe, don't get in. AND once on the track, if your student or their car scares the begeezus out of you, pull into the pits and get out. You owe the student your effort in teaching, not your bodily safety.
If you get in a car with a cage, make sure there's a harness at least. Better if it has a harness, to also use a HANS device... you never know.
NEVER get into a caged car without a helmet, even for parade laps, or novice yellow flag runs. Just wear the helmet!
IF you get to drive the students car, be respectful. You DO need to figure out if the car will do what you want the student to ask of it, but you don't need to go 10/10ths and balls to the walls. You'll probably get the chance to drive some pretty awesome machinery from time to time, but always remember to treat it better than your own.
Just remember to have fun with it. ^_^
Here's a cool video (cool to me anyway) my student posted recently from the last track day. It's got pretty good audio of my typical instruction on a first session of the day:
http://www.youtube.com/watch?v=aaEN5F0YEFk
Some students I need to walk them through each turn...every session... some get it and let them start to put it together. It's interesting sometimes to see them notice their mistakes and correct them.
You can tell by this later session on the same day, I'm more quiet and I try to let him dial it in, and give hints where I can. He was a little timid in trusting the car, but toward the end of the day we sort of got there:
http://www.youtube.com/watch?v=mCcJeVFk3X0
and here for Fun, one student rode with me. We just went out and I try to go generally 90-95% on a warm up lap to get the tires hot, and he was a little afraid. It's not a pretty lap, but it's funny.
http://www.youtube.com/watch?v=3geIv9RU3so