If you have the divider already, simply "glue" the runners to the sides with aquarium sealant, and leave it to cure for 24 hours ( some packs say less time but give it 24 anyway to be absolutely certain). Any excess sealant or smears can be removed with a razorblade. Make sure the divider is tall enough so the bettas can't jump over into each others sides though!
BUT before you put the divider in, cut a hole in the edge of it about halfway up to allow the heater to go through so half of it is on each side. Make EXTRA sure the fish can't squeeze through any gaps where you have cut the plastic, and also make sure that there are no bits of cut plastic sticking off that the fish could catch their fins on .
For a filter, you could either have a small sponge or HOB filter in each half. If it were me personally I'd have a small sponge filter in each half . They are gentle and create little to no current to disturb the fish.
As for easy plants, I always reccomend Cabomba. Tall, soft brushy leaves, perfect for bettas ( you can see it behind duncan and my gourami in my sig , and also in my big tank if you click on the pics ) . Amazon Swords are doing well in the stock lighting of all 3 of my tanks including the betta one, so those are also good and have always been easy for me. The big tall leaves are good for bettas to rest on. Java fern and java moss, along with mossballs all do fine in stock or low lighting. Elodia is also very easy and although it will need trimming off when it gets too long ( Cabomba also ) , that's really all that needs to be done with it. All those plants are very commonly found in most LFS's .