Once you have been doing jiu jitsu for a couple of months now you start to get better. As you begin to understand the basic moves, the sweeps, submissions, passing the guard, you begin to feel more confident. When you start submitting beginners your confidence grows and you enjoy your martial art more and appreciate the techniques you have learnt.
So when can I start participating in competitions you will ask. Competitions are an excellent way to give you even more motivation to train hard. It gives you a sense of accomplishment and also experience in fighting under pressure; under pressure of time and of losing.
In the Brazilian jiu jitsu white belt category you will likely face guys with no experience but also guys that have done jiu jitsu for two years or so. If you walk in knowing very little and you don't have much background in any other related martial art, you will likely lose quickly.
Here I wanted to give some advice on things you can do to prepare. I recommend competing not before you have at least six months of jiu jitsu training unless you have studied or related martial arts in the past (like wrestling or judo).
1. Train more
You need to really train more than three times a week before competition. Sparring is very valuable and you don't want to be gassed during the match. Practice with opponents that you can learn from, that are better than you or about the same level as you. If you are always winning against weaker opponents, you develop slowly.
2. Supplement your training with conditioning exercises
Sign up to the gym. I recommend group interval training to improve your cardio but also strength training helps. You must be fitter than your opponents and good cardio really helps to give you the edge. The bicycle and rowing is very good. They improve your strength and cardio but you also should not overlook the classic exercises like the jump rope, push-ups and pull ups.
3. BJJ oriented exercises
I find it is very valuable to do specific jiu jitsu oriented exercises like grip training. Rope climbing helps you develop strong arms and a solid grip.
Another good example is neck training. Having a strong neck is important for your ground fighting so exercises such as neck bridges can really help.
Also don't overlook the sprawl. You can incorporate it into your cardio-conditioning routine and develop a good takedown defense.
4. Judo
Brazilian jiu jitsu tournaments start from standing. Having a strong Judo background will give you an advantage here as you will be able to takedown your opponent and score points before you start to play your jiu jitsu game.
Practicing Judo once or twice a week to supplement you jiu jitsu will really be beneficial.
If you are training for a no-gi tournament, consider freestyle wrestling instead.
5. Recreational sports.
When you are not training but relaxing with your friends, there are many activities that can also help you develop. Rock climbing is my personal favorite but also you can do swimming, football and pretty much any active sport.
Develop a nice timetable for yourself but don't over-train. If your body is hurting, then rest and recover. You should mix your exercises well to allow different parts of your body to recover before enduring more exercise. If you are really tired, watch some jiu jitsu instructional dvds instead and then go ask your teacher about certain moves you have seen.