What should I wear to my first class? ^
Ideally, you should wear the standard training uniform, referred to as either a 'gi' or sometimes, a 'kimono' (generally only in Brazil: if you're interested in the history of the gi, see here). This consists of a jacket and trousers (typically cotton), designed to cope with the strain of being twisted and yanked. It also comes with a belt, to tie the jacket closed: for your first class, this will of course be a white belt (there are five main ranks in BJJ: see here for more on that).
However, if you don't have a gi yet, it is normally ok to just wear some loose trousers and a t-shirt, or a t-shirt and shorts. Make sure that there aren't any zips or pockets, as those could either scratch your training partners, or catch fingers and toes. You can always buy a gi later, once you've decided you want to stick with BJJ. For some advice on what to buy, see here. Similarly, don't wear jewellery and tie back long hair (see here for more details).
Alternatively, you may decide you'd prefer to go to what's called a 'no-gi' class. As the name suggests, this type of training is done without a gi. That means a t-shirt and shorts is fine, or better, a rash-guard and shorts. For more on the differences between gi and no-gi, see here.
How should I approach class as a beginner? ^
Here are my top five tips:
1. Relax
The biggest mistake most new people make is treating every spar as life or death, clinging on desperately trying not to 'lose', or using as much muscle as possible so they can 'win'. Save 'winning' or 'losing' for competition: in class, just concentrate on improving your technique. It doesn't matter if you get tapped along the way.
Relaxing also helps to avoid injury: if you're so focused on 'not losing' that you don't tap, you're liable to hurt yourself. Relax, tap and start again, instead of holding on until something breaks, putting you out of training for weeks, months or even years.
2. Ask questions
Don't be afraid to talk to people. If you're confused by something in drilling, find the instructor and ask them to help you out: after all, you're paying them to teach you. Similarly, after sparring, if you don't understand what you did wrong, ask your partner. They're in a great position to tell you.
3. Find a good training partner
Following on from the previous point, if you find somebody is particularly helpful in drilling, provides useful advice after sparring, and/or generally stays controlled and technical when rolling etc, stick with them. Good training partners will have a hugely positive effect on your progress.
Of course, a good training partner will normally be more experienced than you. Someone who spouts off without knowing what they're talking about becomes irritating rather than helpful. Having said that, it is possible to learn from anyone, so don't be close-minded.
4. Maintain good hygiene
I can't emphasise this enough. Not only is it extremely skanky to train with an unwashed gi, it's also dangerous. There are lots of nasty bacteria waiting to jump all over your skin in sweaty grappling sports, and infections can even be fatal (MRSA, staph etc).
Stay safe by taking a shower after training, then wash your gi once you get home. I would advise owning more than one gi, meaning that you can wash your gi after every session you train. No-one wants to train with the stinky grappler, and if you come in with infections (be that fungal, like ringworm, or the really dangerous stuff mentioned earlier), you're quickly going to become very unpopular.
Also, be sure to keep your nails short. Otherwise, you're liable to cut people, which again is not going to impress your training partners.
5. Keep training
BJJ is a difficult sport, and that means there is a high turnover of white belts. Lots of people start, get frustrated, then quit. Accept that the first few months are going to involve a lot of you getting squashed under somebody else. Stay consistent, eventually you'll get the hang of things.
For an excellent list of advice in a similar vein, see BJJ Grrl's "Dos and Don't", or for another superb set of tips, Levo's old piece on beginning grappling. Finally, read Georgette's advice on staying clean.