So, my first experience with time limits was when I got into band photography a few years back - actual bands, and not just messing around at the local bar. Before this event I took my time, made sure to get every shot I could, and generally didn't work with a urgency. After this event I learned that clients can, may, and do request that I have "3 songs" and done, and in that time I need to get everything I can, because when they say done, they mean done.
That said, this is also talked about in an interview with David Platon where he said he had about 10-15 min with Russian President Putin to take a portrait (granted all the gear was setup). Which, would give some hobbyists heart attacks, both on the count of the person, but also the time frame.
So for bands, it really is about 2-3 songs and you're done. After that the bands get sweaty, lighting changes, and for the most part they don't want anyone up there in the way for their whole set. Now, don't worry too much, since a lot can be done in that 10 min span, and good shots can happen.
Also, you run into the CEO who only has about 20 min to sit for the headshot, which although more time than a person needs, it also means that nothing can go wrong and everything has to be planned for. Or, when you're shooting some figure skaters and you literally only have 15 min of ice time to setup lights and do the shoot.
RULES OF SHOOTING FAST!
Learn to get yourself in the best positions, and take advantage of them!
I had no idea Wayne was going to do that, in fact I wasn't even a big Flaming Lips fan before that concert - but - after dodging all these balls and stuff in the air - I kept myself around the center of the stage and on him, shooting at moments he and other band members were doing something interesting.
Never give up!
That shot was the last one I took of MIA when she was here a few years back. It was literally the last shot I took before the stage managers said the time was up. Now, the never give up part comes into play because it's hard to get a good shot of someone with dark skin, white hair, under green lights, when they move around a lot... So, if you have only 15 min of time, use all of that, or at least go until you're very sure you got what you need.
Have the equipment for the job, and have backups!
Planning for the shoot is a must! You never know when something is going to break, or even more common, when something is going to be needed. It's better to plan and bring too much than go do it and wish you had something. This also includes for on location work talking to the clients and/or even going there before hand to make sure things can be done how everyone wants them - and that everyone is happy with the choice.
For example this company job I did a few months back, we were doing a portrait of the CEO in her office, and it had some off color walls. You better believe that I was up front in an assertive way that the background wall color was something they would be happy with - and even then I made sure to bring paper and a backdrop stand just in case. I also packed and used my battery pack, so I didn't have to worry about an outlet or something that wasn't accessable.
For band photography, although I don't use it that often, I make sure to bring my 50 1.4, since you never know when 1/60th iso3200 f2.8 isn't going to be enough. Going back to the MIA shot again - if I didn't have the 50 there was no way I was going to stop motion and get a decent shot.
Practice, practice, and practice!
If you don't feel confident to do any shoot (just the shoot, not setup) in 15-20 min, then it may not be time to take on that kind of work. I'm serious here, since you never know when something is going to come up, when this lighting style you had in mind wouldn't work, and when you really need to pull on experence to get the job done.
I'm not saying hunker down in your basement and don't come out for 10 years, but having an understanding of lighting, what to do if someone has glasses, or if what you planned wasn't working out.
Build a rapport with the person.
This was a shot of someone who, although knew we were doing pictures that day at his work, wasn't a model, and who needed to be comfortable in front of the camera. Now, this is something I'm not great at describing, but making a connection with the subjects is a must!
personally I tend to take the "I'm a professional" approach, and assure them that I know what I'm doing, I'm not worried, and I'm not stressing out, and that this is fun for me - then just joke around a bit while taking the pictures. It's easy to get someone out of their shell, to smile, and to get a good shot, you just need to do that and be comfortable doing that fast.
I think we did about 18 people in 2.5 hours that day, which was faster than the full day of shooting that was planned out.
Know when you got what you need!
This may go against the "never give up", but keep in mind the goal of the shoot and know when you attained it. That way you know both when to call a wrap, but also when it's time to calm down a bit and be more creative - since you know you have what is needed. In that series I talked about above, where we did 18 people in 2.5 hours, I only took 4-5 pictures of each person max, and once I got a good few shots then I knew it was time to move on, get them back to work, and get the next person in.
If you're shooting bands... NO FLASH!
That's right, learn to use no flash for live shows - since that's the way they are done. Flash is annoying, it gets in the way, and almost all live performers don't like it. So you're faced with 3 songs, no flash, and once the time is up you're done (period).
This just went from something that sounds fun to a really stressful night in a hurry!
Expect to do the job fast.
Finally, just treat every job like it's urgent and like the persons time is valuable. I'm not saying you need to rush things, or that you need to be frantic, just to keep track of time, and don't drag things on if you don't have to. That way you're ready for the "you have 2 songs" or "they have a meeting and need the office in 30 min" or "our ice time is up in 10 min".
For example, in this series - http://www.andrewthomasevans.com/photo/redlight.htm
She told me, after being late due to traffic and weather, that she only had about 30 min to shoot. Which was kind of alarming in a way since I never did shots with a red light like that before, so it was new to me, and this was the first I had heard of it. Anyway, to make a long story short, I was able to get what I wanted, learn about that process, and get some successful shots within that deadline, and she was able to get to her meeting in time.
I don't think I could have done that, my business headshots, skating shots, or even some of my outdoor work if it wasn't for that first "you have 3 songs" job.
So I hope this was helpful in getting you ready for that first call where they say "you only have 3 songs" or "you have 15 min to shoot this."