Adding live plants to your African dwarf frog habitat has many advantages.
Aside from giving your frogs natural-looking places to hide and making the habitat more interesting and attractive, plants help remove ammonia and nitrates from the water and will help slow nitrate buildup. This may result in less-frequent need for water changes.
I mainly keep plants in my aquatic habitats for the water-quality benefits, so one of my favorite aquarium plants is hornwort. It's one of the most effective of all aquarium plants at sopping up toxins. It also can be used either as a "rooted" plant by tying it to a rock or suction cup and anchoring to the bottom, or it can just be left floating at the top of the water. It's one of the easiest aquarium plants to care for.
Practically any freshwater aquarium plant will work well in an ADF habitat, however. Unlike turtles and some fish, frogs tend not to be interested in aquascaping, so they don't uproot the plants. They also tend not to eat them. In addition to hornwort (mentioned above), some of the best plants for an African dwarf frog tank are also some of the easiest to care for, such as:
If you're just getting started, you might want to consider buying a package of assorted aquarium plants. It's a quick and easy way to get your habitat planted in a way that's interesting and natural-looking.
If you have no interest in plants other than to help keep the water clean, you can just go with some floating or anchored hornwort and a real Marimo ball or two. They require practically no care, are nearly impossible to kill, don't need a substrate, and will help keep the water clean and healthy.
I advise new keepers to stick with simple, inexpensive plants that are easy to care for. You'll still be learning to care for your frogs. You don't need to add the task of learning to care for delicate or hard-to-raise plants at this point. Any of the "beginner" aquarium plants that you can find at your local pet shop should work and your frogs will like them just fine.
All plants require light, but not all plants require special plant lights. Most "beginner" aquarium plants will survive well enough with nothing more than a standard aquarium light. If you want the plants mainly for their water-quality value, then that's probably all you need. If you decide to venture into more exotic plants, however, or if you just want your beginner plants to grow their best, then you should consider installing an aquarium plant light.
The only substrate I use aquatic tanks in which I want to plant rooted plants is Flourite. It's the reddish-brown substrate in all the pictures of my own frog habitat on this site.
Flourite is basically a clay gravel that has excellent characteristics as a substrate for both plants and friendly bacteria. It's also very attractive and relatively trouble-free to maintain. Other than vacuuming, it requires no special maintenance.
I do have to warn you, however, that Flourite gets very dusty in shipping and MUST be rinsed before using it, otherwise the water in the tank will look like chocolate milk. Even if you do rinse it, it will still severely cloud the water for a while. It'll just clear up much more quickly if the Flourite has been rinsed properly.
The best way to rinse Flourite is to place it in a five-gallon bucket (fill it about halfway), slowly fill it with water, stir the gravel, and let it overflow until the water coming out is clear. I usually do this outside using a garden hose, but I've also done it in slop sinks and bathtubs during the colder months. There's more about how to actually install Flourite in your tank on this page.