I'm not sure what type of lighting your ten gallon aquarium has but try to find and purchase a plant friendly grow light. The pet store is your best bet unless your tank light is not flourescent. Most plants require lots of light and standard bulbs do not provide the right kind of light.
I always had healthier freshwater plants when I kept the tank around 74 deg F instead of 80 deg where I typically keep my freshy tanks.
The single biggest problem I had with freshwater plants is trying to grow and keep them healthy without be over run by algea.
Algae loves phosphates and my local tap water has 1
ppm phosphates. If you are not sure about your water buy a phosphate testing kit. There are a few products on the market that help absorb phosphates out of aquarium water, you may want to get one of these products.
You do not have to re-
cycle the tank, just keep dead leaves and debris cleaned up in the tank. If you are not going to keep fish in the planted aquarium then you will need a plant food supplement. I did not see any real improvement using plant foods when I used them in tanks with fish.
Don't be afraid to trim the plants especially if leaves begin to turn brown or die. Healthy plants grow very fast.
I always had good luck with plants rooting well in small aquarium gravel. The larger gravel did not work as good.
Plants need the aquarium water to circulate but not aggressively. If you are running an undergravel filter you may want to have a small air stone to keep the water moving, but again not a whirlpool.
Lastly don't panic if your new plants shed several leaves in the first few days/weeks after purchase. The plants are adjusting to your water and will grow new leaves that better suit your water.