What is commonly used is a little bit of everything... what is actually successful may be a completely different story! First thing I'd like to bring up is that mosses typically do not make a good groundcover... it both goes against what is best for the frogs and is honestly the hardest and worst place to try and grow moss in a tank. Frogs typically hang out in, around, and on leaf litter (with the exception of the truely arboreal) where the moss is clinging to trees and rocks trying to get sunlight where it can. In the tank this translates to leaf litter on the floor, and mosses on the non-living cage furniture. Very natural, very cool, and MUCH easier to get the moss growing on substrates that aren't holding any water, better light, generally less trampled, and less of the vitamin/mineral/calcium powders so well known for killing them.
While some people have collected native mosses, I recomend against it. Partially due to native mosses being seriously over collected, and partially because it's much harder to find a native moss that does well in the tanks other than a couple places that heavily frown upon collecting green growing things... these mosses mostly die, may survive but often don't thrive (spread like a carpet) or spore - sure signs that they weren't the best choice.
Other options include buying pillow mosses and tropical mosses by the foot, mostly to take advantage of those trying to make moss lawns in their tanks. I know Black Jungle's tropical moss tends to be incredibly popular because the stuff thrives in frog tanks (the same stuff may be available thru other sources), but the pillow mosses, while pretty, are rather touchy, or it may be just because of where they are put in the tank. Tropiflora and black jungle supply both I believe, and they can probably be found from other suppliers.
"Aquatic" mosses are also becoming popular... where the pillow and tropical mosses won't live/thrive because it's too wet and they rot out, the "aquatic" mosses (all of except one is actually semi-aquatic and can be grown both aquatic and terrestrially) when given lot of light will thrive and spread. Because they are uncommon, they can be a little pricey for a small portion, and do not give the "instant gratification" that the square footage of the mosses above can give, but in the right conditions they spread well and will take over all the spaces that are to their liking. These are often bought thru aquatic sites, aquabid is a good one, but some sponsors on here have also started supplying them in small amounts too.
Kyoto moss spores are also being tested in some tanks... they give a nice look of soft green velvet over surfaces they germinate on, but it can take a long while. After the long time getting established, it's supposed to be pretty good about spreading to all the places in the tank it likes. Seems typical that, coming from the Bonsai trade, these spores will teach you patience! These are found from Bonsai suppliers and eBay.
My personal batch(es) of moss were mostly from a local friend who years ago had gotten some collected tropical mosses. Must be 5 distinct mosses in the mix! They are obviously tried and true mosses! I have simply taken his recomendation of introducing a patch (maybe a square inch or two) onto some top part of the tank near the light. Once the mosses get established, you'll see the patch spreading, and I have also found mosses popping up all over the tank! I was told this may be in large part due to the frogs possibly tracking spores all over the tank, and by having the moss at the top helps - gravity spreads it down