We rescued a kitten that was abandoned by its mother and it's eyes are very runny and they have green discharge. The kittens belly is also very distended (swollen). What can I do to treat this at home?

I think you should take it to a doctor, why would you try to treat it if you don't know what to do? VET!

Definitely take it to the vet. It sounds like it's sick, and might have worms, amongst other things, in which case it will probably need medicine.

My dad rescued a kitten like that once that died three days later.

If you care about the kitten, taken to the vet ASAP and see what can be done...

I will add, though, that a distended belly can also be a sign of starvation. If it's very young (nursing age) you can try giving it milk, but make sure it's whole milk because low-fat milk could make it sick. If it's a bit older give it some mashed up meat or something...