Learning to fight involves learning two different areas of self defense. To be a complete fighter and be ensured of good self defense skills, learn the basics of both the following:
1. Standing up and Striking.
You need to learn basic striking skills in order to handle yourself on your feet. This will include punching as well as defense techniques like covering up and blocking strikes.
Another aspect to standing up and striking can involve the use of kicks. Learning different kicks can round you out as a good stand up fighter. Kicks can be effective on the street as well as they widen the gap between you and your opponent, backing them up so you can gain control and make a strong offensive next move.
2. On the ground and Wrestling/Submission.
Many don't realize that most street fights end up going to the ground. This is a very important area and can easily determine the winner or loser of a fight. Even if you get struck standing up, you can completely reverse the situation by taking control on the ground.
You can also learn take down skills to get your opponent on the ground where you then can apply effective wrestling or submission moves. Learning ground submission skills can immediately end any conflict. You can learn a few choke holds and that will end the fight.
To be a complete fighter and be confident as such, you need to learn both standing up striking skills, and on the ground wrestling skills. Learning mixed martial arts style training can cover both of these areas effectively and quickly.