I have Red Cherry Shrimp, so I can tell you a few things bout keeping those...
Don't have lots of plants in your tank. If the tank is less than 10g then don't have any plants in there apart from Java Moss. The shrimp love Java Moss, grow lots of it on rocks - preferably rocks instead of drift wood as the shrimp aren't big fans of tannins. Make sure the tank has lots of things for the shrimp to climb on, they hate bare tanks, and also give them lots of hiding places. Each shrimp needs its own personal hiding place.
Try to get your water to the right parameters BEFORE you put the shrimp in the tank. Red Cherry Shrimp are hardy and can live in most parameters, they just hate it when their parameters fluctuate.
Ideally you shouldn't have any fish in with the shrimp, especially at first when you are trying to create a new colony. Even if the fish aren't trying to eat the shrimp, their noseyness will stress the shrimp.
Use a spong filter, or at least a piece of sponge over your filter's intake to avoid deaths that way. If your filter/pump return is pretty fierce, try to slow it if you can or point it against the side of the tank. The shrimp are strong swimmers, but wont necessarily appreciate being battered!
Don't over feed. When you first get your shrimp, don't feed at all. Leave them a few days to settle in. Remove any excess food. I've been using Hikari Crab Cuisine and they love it.
Trying to think what else you should know...
As for temp, they do fine between 70-80F. Red Cherry Shrimp seem to like pH around 7.2.
When you first get your shrimp they might go AWOL for a day or two. They are just adjusting and are slightly stressed. I found an exoskeleton from one of mine and like a total n00b thought it was a dead shrimp! But, what that does mean is that the shrimp will now hide until its new shell has developed.
Feel free to ask anything else.
Sorry, forgot to explain about why you shouldn't have lots of plants. They can suck up a lot of the nutrients that the shrimp actually need for their shell.
Also as another nice treat for the shrimp, you can sink water logged dead (brown) leaves into the tank. Just one at a time though. The shrimp will feed off the bacteria that colonise the dead leaf. Just make sure the leaf is definitely brown and waterlogged (soak in a bucket for a few days) and that the leaf isn't contaminated, i.e. only take it from somewhere you know it hasn't been exposed to any pollutants.