How does someone prepare for a BJJ tournament, especially when the person is gassing out after the first minute of the first fight? What could be the reason of gassing out? Is the overtraining him-/herself or does he/she needs physical training?
I second Dave Liepmann's opinion about adrenaline. It likely is an adrenaline dump. And yes, competing more will help. It will lessen the nerves over time. Learning to calm yourself down before the match will also help. So, deep breathing exercises and doing something to take your mind off of it.
Aside from that, if it is physical rather than mental, then there are multiple issues that can be looked at.
First, ask your doctor. This could be an indication of a heart problem. Maybe a leaky valve or a misfiring of nerves that control the heart. It could also indicate high or low blood pressure. Or maybe a problem with electrolytes in the blood. You won't know until you've gotten yourself thoroughly checked out. And there are such things as sports medicine doctors. They have tests that can see how your cardiovascular and respiratory system are responding under stress. That can reveal problems that wouldn't be seen if you're in a resting state.
Second, conditioning. Obviously, if someone isn't used to going all out for several minutes without end, then that's something to work on. Weightlifting can be helpful, but switch to fast power lifts and high rep work. As opposed to low rep, slow lifts. And employ supersets with no rest between supersets.
Adding a running regimen to your conditioning is one of the best things you can do for cardiovascular stamina. You should add sprints once or twice a month (more than that won't be very useful). Go all-out with the sprints: 20 seconds all-out, 10-20 seconds rest, then repeat. Do that for 6-8 reps. It is exhausting, and many people quit after just the first 3 reps. That's to improve cardiovascular endurance, rather than just stamina.
Consider uphill running. And consider buying a weighted sled and/or parachute for getting some resistance while running.
And yes, over-training is a problem. No more than two days of training in a row. Take a rest day after that. Better yet, one day on, one day rest, and repeat. One week out of 4 weeks should be a low intensity week. Also, take several days to one week off right before the competition.
Third, nutrition. Not eating before the competition is a problem. You need energy. So eat. Drink water, too. You don't want to be dehydrated. And don't down a bunch of caffeine or anything else that might pump you up and then dump you. I'm not a fan of energy drinks. I think there's too much potential to screw people up (adrenaline, heart racing, etc.). And they can become habit forming, thereby losing any benefit they might give you anyway. But something like regular Gatorade would be fine.
Anyway, those are my thoughts.
You probably gassed because you experienced an adrenaline dump. Solution: compete more.
If you're training a lot then overtraining might be a culprit, but that's more easily evaluated by looking at the person's training schedule than the single data point of "gassed out in their first match". If you're not doing any out-of-class strength and conditioning and you're training less than five times a week the issue is probably not training enough, not training too much.