In the wild, larvae eat anything the right size, which is less than 5 microns. Micro fauna, aka infusoria of some kinds, plankton, single cell algaes.
You can feed them cultured single cell algae, aka green water. It will suit larvae quite well. I've raised a number of them using this. Once morphed, they can take microworms, which are a great food for them, or Golden Pearls, in the 5-50 micron size. Small amounts, they are very, very tiny when first morphed.
Make sure they can't be sucked into a filter. Sponge filter is best. Females and males can be hard to tell apart, but once a female saddles, she'll moult and you'll see eggs very soon after that. Moulting females send out mating pheromones. She'll carry the eggs for a few weeks, and they will get larger and lower down as time goes on.
Eventually it will look like she has strings of pearls on her swimmerets.. and then they fall off and vanish.
Depending on temps, they morph roughly four - five days later. The eggs float to the surface very quickly, where they soon hatch, and that's when feeding is most critical, during the short larval stage.
After they morph, they hang at the surface upside down for a few days, in daytime. Once the lights go out they sink down, looks like they are riding a spider's line. Light makes them rise up again. They don't swim for a while, but if worm or food item gets close you can see the tiny body jerk as it grabs it. You can see the eyes, the hump and sort of see a suggestion of legs and whiskers. They moult often, you'll see shed shells floating and think they are dead shrimp, like I did at first.
Once they can swim, they soon begin to forage like adults. They do best in a tank that is mature with lots of biofilm. Sponge filters are popular feeding sites, as is wood in the tank. Moss is great too.. They tend to stay low for awhile, until they grow a bit more.
Temps around 70-74 are good.. they like it on the cool side.
Edit.. I fed mine about 50 CC of single cell fresh water cultured algae twice a day until they got to the stage where they could swim. Used a big plastic syringe to just inject it along the surface of the water. I get the alage from a lab, Florida Aqua Farms grows them, and while they are not cheap, you can reculture over and over again from one disc. The bottled or bagged type is usually in salt water, which will not work. Has to be fresh water. You want Japanese chlorella, aka Nannochloropsus.