Berin Loritsch has a good answer, but I wanted to add something here as well, as one who primarily has trained in standup martial arts, but also had spent some time training Brazilian Jiu-Jutsu in an MMA gym as well.
If you are on the ground and primarily train an art that emphasizes standing techniques, and are engaged against someone whose art has them primarily train while fighting on the ground, they will by default have an advantage due to their specialty. While you can, and it should encouraged, to train your techniques so that you may use them in as many situations as possible, which may include on your back on the ground, your element is fighting while standing. Try to keep the fight standing as much as possible. There, if your opponent is not as trained in standing fighting as you, you will have an advantage.
It also is good to mention that while an art may emphasize standing techniques, often they may incorporate or include some ground techniques as well. This may not be as common, depending on the origin of your art or its purpose (for instance, Judo has a very strong tradition of ground techniques, but Savate probably won't). If your style includes some ground techniques, you already have an baseline from where you may expand or experiment (of course, with a partner who knows what he's doing, and not in isolation). Cross-training in different styles also can be encouraged, if you are experienced enough.
From my experience, my kung fu training was primarily stand up. However, we had a few techniques that had us on the ground, as well as a "laying stance", in which we were on the ground on our back. The techniques that I was exposed to was limited, but there was a small variety. They mainly were concerned with being able to get back up quickly to fight. When I trained for several months in Brazilian Jiu-Jutsu, I found, to my delight, that the ground techniques I learned in kung fu translated very well to BJJ ground use. For example, the "laying stance" that I trained was very close, with some slight modification, to open guard. While my kung fu training only had limited help with situations focused on fighting on the ground, it allowed a very easy transition into the techniques that Brazilian Jiu-Jutsu trains you for ground fighting.
In the end, each style has its own emphasis and specialty. No one style is the end-all and be-all of all aspects of fighting. You can adapt some techniques for use on the ground, but ultimately, they are not always going to be sufficient when up against someone trained in ground fighting. Of course, if you want to try and train these techniques specifically against ground opponents, it is best to, at some point, train them in sparring against someone who is skilled in ground fighting.