Plants need light in the correct spectrum, and food. They can get some of that light from sun. There are LEDs that work spectacularly for plants, and ones that don't have enough/too much power. CFLs also work. I have four different lights, 3 LEDs and one CFL in a swing arm desk lamp.
The CFL works great (6700k bulb), one of the LEDs is amazing, one is too much light, and one is too little. You can figure out your LED just by observing your plant growth, and adjust if necessary.
Plants get some food from fish food and poop. Usually, in a well maintained tank with a single Betta, that isn't enough. So, you need either root tabs (for root feeders), or fertilizers you add to the water (for water column feeders). Anubias and java fern are water column feeders (no roots below the soil). Swords are heavy root feeders (lots of roots in the soil).
Depending on what plants you end up with, you will need root tabs and/or liquid fertilizers.
Don't run your light a billion hours every day. It just creates algae. People frequently do a split with lighting to try and control algae. Say, four hours on, two hours off, four hours on. You can use a light timer for this. Algae tends to be a symptom of imbalance, so be patient when you see it and just try to figure out how to get the system back in balance.
It's a really fun hobby, so enjoy it! Fish loooooove real plants, and they look so great.