I've driven type 2s (vanbulances) and type 3s (van front, box back), and here's my line of tips.
A lot of ambulance driving is the same or similar to regular driving practices.
Take turns slowly, especially in the top heavy, narrow base type IIs . Until you get used to it, if you think you're going a good speed, you're probably going too fast.
When stopping, when you're almost stopped, let up slightly on the break. This will allow you to expend the rest of your energy going a few inches forward instead of going forward onto the springs, and then rocking backward.
Remember, you can't hit anyone if you're stopped. If you're in any situation where you can't accurately predict what the other cars are going to do (like a Mexican standoff), just stop. Either they're going to go or they're going to signal you to go. Not being in an accident at all is better than being not at fault in an accident.
For type 3s, your mirrors protrude past the box, so if the mirrors make it, your box will make it.
The ambulance will fit into a parking space. If you know your parking space is clear, line up the left tire just inside of the left parking space line and use the line to guide your backing. You still need to watch the back to know when you need to stop, but as long as your tire is lined up, you're inside the parking space.
If you're on the freeway and going freeway speeds, remember a buffer space. I'd argue 4-5 seconds is good. Also, use seconds, the nice thing about seconds is the faster you go, the larger the gap.
More for type 2s again, be slow on the accelerator and slow on the brake to avoid hard stops and hard starts. There's nothing wrong with starting a slow break a little early or being slow off of a green light or stop sign.
For emergency driving:
There are prizes for second place, however there are no good prizes for being in an accident. If what ever you're going to do has any decent risk of causing an accident, you probably shouldn't do it.
In urban and suburban environments, the siren is essentially only good for cars on the road you're on. Cars coming off of side streets? They probably haven't heard you well enough to know you're on the street they're turning onto or crossing. Never assume that just because the siren is on and loud to you that others have heard it.
Again, if you need to, stop and let tricky traffic situations work themselves out.
Do. Not. Tail. Gate. I don't care that the idiot in the car in front of you isn't yielding as fast as you'd like them to. If you tail gate, the only warning lights visible are the headlight flashers (wig-wags) if equipped and the grill lights. To be honest, the grill lights aren't always that visible, especially during the day.
If you're coming up on a red light, look to the left. If the opposite lane of traffic is empty, go into that lane. Going down an empty lane opposite of traffic where the closest traffic is stopped at a red light with an unopposed view of an emergency vehicle with lights on going the wrong way is INFINITY more safe than trying to force cars into an intersection against a red light.
Standard suggestion: Make all turns from the left lane. Turning right? Try to do it from the left lane. Turning left? Do it from the left lane, you're more visible there.
Try to pass on the left, but sometimes you have to pass on the right. It happens, get over it.
Finally, one of the golden rules of life. Just because you can doesn't mean you should. We should never be a greater threat to our patients than their disease, and any accident is a greater threat. While we may not always be at fault, often times we can contribute to an accident not happening by good defensive driving techniques, even if it means giving up a right of way that is rightfully ours. There's no prizes for an accident and no prizes for forcing someone to submit to your lights and sirens. If it's unsafe, simply don't do it.