Fighting on the ground
In most self defence situations, it is a good choise to avoid going to the ground. The ground may in and of itself be a threat to you, as the surface may be rough upon impact, or there might be shattered glass or something else which can cut you. The other aspect is that it is difficult to move on the ground, which makes escaping the situation difficult, and if another person attacks you with a kick or a stomp, it will be difficult to avoid getting hit
Having said that, it’s naive to think you can always choose to avoid going to the ground.
For this reason, it is great to practise ground fighting, and I highly recommend either taking up Brazilian Jiu-Jitsu, or learning a few essential techniques from that source.
Just remember that you don’t always need a fancy technique, and that brutal direct methods such as eye gouching and going for the throat, might be necessary options. There’s a reason why so many traditional martial arts, as well as krav maga, employ such strategies.
Bringing your opponent to the ground may be a good idea, if you can manage to remain standing, as it will allow you more time to escape your attacker.
To learn how to bring down a standing opponent, as well as how to escape from the ground with an opponent on top of you watch this video.