Can I float this plant?
Yes, it'll actually grow into a nice mat when you float it - but the stems take awhile to straighten out if you grow it floating for awhile and try to plant it. I had some floating for over 3 months in my 110.
If not, how exactly do I plant this? I got my package of it in the mail yesterday, and I just put eco complete in a tray and tried to plant it with tweezers. Didn't work too well, it's hard to distinguish the roots from the stems. How would you recommend it?
Any stem that you stick down in the gravel will grow roots, so don't worry too much about telling them apart. Stick the stem in far enough that it'll stay put and you should be fine. I generally poke it into the substrate with my fingers and if any stems are much taller than the others, I pinch those off and stick the stem down into the substrate with the others. It'll grow roots fairly quickly.
As of right now, some of it is floating. In emersed growth, you don't want any water about the substrate level, correct?
In my current setup, it goes from water JUST visible over the substrate when totally full to water 1-2" under the top of the substrate. It always stays wet though, Soilmaster sucks up water and holds onto it very well, so it is always moist. I think this is the kind of thing you're going for. Some of my plants, when I first put them up there from submerged growth, get very crispy looking (bacopas, hygros, HM, hydrocotyle), but once they settle in they throw off leaves that seem better adapted and start to grow very well. There are two forms of most aquatic plants, and it takes awhile to convert to the emersed form. Many people I've heard of start with water 2" above - like you are doing - and then let it evaporate until the plant is exposed. As long as it doesn't completely dry out crispy, it should start converting and sending out emersed leaves. Some will look a bit crispy though.
Should I keep it covered? I plan on growing this using shaded sunlight, but it's raining today so I have it sitting under my 2 x 55W PC light for now.
I have heard this helps, but I don't think it is necessary. Just make sure things stay humid by misting and keeping the water topped off. I have my emersed plants under a spiral CF bulb (not sure the wattage, 33 I'm guessing) and they really like that. I have 65 watts over the main part of tank.