Take a low-to-average dose so you can be in the same headspace without being overwhelmed. Recently, I tripped with a group of people that included a friend who had "hippie-flipped" (taking LSD and ecstasy together) but never done LSD on its own. Knowing that I was knowledgeable and experienced, she asked me if I could make sure she stayed in a positive mental space. I was confident in my ability to do so, but by the time she was crying because the clock was moving backwards, I was way too stoned to even properly identify her emotion. Luckily the Boyfriend stepped in and calmed her down, but both she and I were lucky to have him around. In a situation where you are the sole caretaker, make sure that you're not incapacitated by your chemicals. However, I do recommend that you be tripping to some degree-- the sense of disjointedness in your mental spaces can make your charge feel misunderstood, too-closely observed, or just generally uncomfortable.
Take requests. If something is making someone uncomfortable, do something about it. Something totally normal while sober (music, colors, light, sounds, TV shows) can cause some real anxiety or fear or discomfort while tripping. On the other hand, if they ask for some specific stimulation (their favorite band, a TV show, etc), it may be the perfect thing to blow their minds. It's your responsibility to help them have the best trip you can, so if it's within your abilities, try to grant them their whims.
Observe general safety. Make sure they don't do anything ridiculously stupid. Even if they really want brownies, don't let them use the oven. Be careful about trampolines. And if they insist on driving somewhere, tackle them and tie them to a chair, because that is a very stupid idea. Like in tip #1, you aren't your mother, but they are trusting you to give them a little push if they need it. Don't let them do dumb things. Very simple. If you can't do this for some reason, skip to the last tip.
Most anxiety surrounding psychedelics is related to the fear of bad trips, which do happen occasionally. Even when it's not a full-blown freak-out, most people do experience unpleasant feelings while playing with their consciousness, and this is the point where it is important for the sitter to step in. First step if things start going badly: ask if they want a hug. Most people, especially while tripping, will appreciate a physical gesture of affection, but others may become VERY uncomfortable with physical touch in this sensitive mind-state, whether it's due to some sort of past trauma or just drug-related paranoia. If they say yes, hug and cuddle away. If possible, and with permission, a cuddle puddle with multiple people might be mind-blowingly awesome. :)
If necessary, ask questions. But not too many. If your charge becomes visibly uncomfortable, or expresses anxiety or confusion, ask them in an understanding way what is bothering them and then do what you can for them based on their answer. However, you have to be careful not to pester them or make them paranoid: I find that answering too many questions (whether I'm tripping or at the doctor's) tends to make me nervous that something is really very deeply wrong. If they are too far-gone to answer (it's happened before) but still look uncomfortable, try distinctly non-sexual but reassuring touches, and experiment with changing the surroundings to see if something there is distressing them. Beyond that, improvise and do what you can.
Stay calm. This should be obvious, but tripping people especially will piggy-back your emotion. Even if there's a pretty good reason to be nervous, don't freak out or your charge will freak out even worse. It probably isn't even as bad as you think it is. Most of the worst trips clear themselves up eventually once sobriety starts to set in. And it might not even be a "bad trip:" everyone (including the positive-minded and experienced) hit little bumps. It's part of the journey. If you're experienced enough to be a sitter, you already know this.
In an absolute emergency, do what needs to be done. Cases like these are really rare but not unheard of. Remember, LSD isn't illegal once it's inside you, so if your friend breaks a leg or is uncontrollably running around the neighborhood naked or gets mugged, call the relevant authorities and tell them all the details. Especially if you need an ambulance: the EMTs need to know what is in your friend's body so they can do the best job they can for him or her. If there are no illegal substances or items on you, you have nothing to fear.
I hope this guide hasn't made you too nervous to do your duty as a sitter, while also presenting you with some worst-case scenarios to avoid. If you have any specific questions, you can ask in the comments or e-mail me at email@example.com.