General Info:
General rule of thumb, 10gal/per crayfish minimum. Individuals can be kept in smaller tanks, but don't overcrowd with other inhabitants.
Keep the temperature between 60-78, aim for the middle. And keep the pH in the 7 range, aim for 7.4 - 7.6 (in the 6's or 8's and it starts becoming harmful to the crayfish).
Provide multiple hiding spots (caves, PVC pipes, rocks, etc) for the crayfish to rest, molt, hide, etc in. Not providing hides can cause stress in a lot of species and individuals.
Select tankmates carefully. Usually a "blue crayfish" is a P. alleni, which generally resides more on the carnivorous side and aggressive side in comparison to other species (temperament ranges in individuals though), meaning it's likely to actively hunt. So, don't put anything with it that's going to be a problem if it ends up as a meal.
Feed a variety of foods to give it a good range of nutrients. Things like carnivore, algae and sinking pellets. Veggies, plants, meat scraps (be careful, meat fat will leave a nasty oil on your waters surface), etc. Give them a source of calcium (eggshells, cuttlebone, uh... Ken's came out with an invert food that has calcium supplements in it). Do NOT feed them shrimp or shrimp products unless they have been cooked/processed at high temperatures or freeze dried several times (shrimp can contain WSSV and other diseases that are fatal to the crayfish).
Get a lid for your tank and seal up any holes, if you haven't already. Crayfish are excellent escape artists and like to go exploring outside of their tanks.
And most importantly, enjoy. Crayfish are totally awesome pets! They have a variety of quirky behaviors, can be taught to do some very minor tricks (with the incentive of food) and are just really fun all around. ^_^