Congratulations! You have been selected to fill a very challenging position, and should be extremely proud of your abilities and (seriously) giant wealth of knowledge. If you've never done tutoring before - or even if you do have a lot of experience subject tutoring - you should know that drop-in is completely different from any other teaching position. It's never the same night twice, and every new face brings an unexpected and totally unpredictable challenge to surmount. But, with that said, I want you to know that the long, chalky hours you spend fielding math questions will be some of the most interesting and rewarding of your tutoring career. I've been at it for two quarters now, and while I realize that's not terribly long, I feel as though I have already learned a TON about how to succeed in this highly improvisational job. So, here's a few tips to help get you acclimated:
First, time management. From a students' perspective, waiting forever to be acknowledged is alienating and frustrating. Greeting each person as soon as they arrive with a "Hi, can you sign in before you sit? Thanks. Oh, and what class are you in?" is not only less intimidating, but prepares you for the depth of their questions. Usually, I work first come first serve, and on busy days you MUST work through the list in order, taking care not to get stuck too long with one student. And remember that you can play the order by ear sometimes, if some students are more confident (or need less attention/reinforcement) than others.
Grouping students by class will also save you significant time when drop-in is crowded. More than once, I've pushed students in the same subject together simply out of convenience for me, and they ended up studying collaboratively and actively helping each other without further prodding from me. You know how in the LSS training class, they encourage you to implement group work in your sessions? Do it. I thought at first that it wasn't possible in such an individualized setting, but trust me, it works, and it saves you having to rework and re-explain problems.
Now, for the moment of truth. My biggest piece of advice to you is this: accept that you may not know everything, and that is ok. Despite the exasperated look they'll give you, you must remember that telling a student you're honestly unsure doesn't make you a terrible tutor or a terrible person. You're an undergraduate, not a god, and blanking on a minute aspect of pre-calculus is perfectly alright. Remind them that math is about thinking creatively and persevering in problem-solving, NOT about having immediate, simple, 'right' answers. Work with them to attempt a solution, and go with your gut approach. Ask other students in the same classes to validate and expand upon you and your tutee's ideas. Let them help you help them! My best ever drop-in was the night a physics major helped me explain an algebra problem to a Math 3 student. Because you're tutoring such a large range of mathematics, multiple opinions and approaches benefit everyone in the room.
You're still responsible for all material, however, so be as prepared as possible! Whatever experience in math you've had, use it to your fullest advantage. Bring old notebooks, flash cards, and cheat sheets for reference, and spend time beforehand brushing up on those related rates problems you don't really remember. I bring colored chalk, a sheet of common derivatives and integrals, and a trig sheet (it's got the unit circle and useful identities) to each and every session. I also have a laptop or tablet handy at all times, to check Wolfram for correctness or to help them look up vocabulary. Showing students how to use resources wisely is part of being a great tutor, since you're aiming to teach them effective study skills as well as math. Ask them to explain definitions to you; turn them back to their textbooks and notes for examples. I frequently offer to email students copies of my formula sheets. Again, it's important to be a role model academically - and friendly too!
In closing, enjoy your nights as a drop-in tutor. I certainly have! I have regulars most every weekend I've gotten everything from quiet thank yous to giant bear hugs in gratitude. Be prepared for anything, and don't be afraid. Working with students is a blast! You never know what you're going to get in drop-in...and that is incredibly exciting. Best of luck, you got this!