Try to place in full sun if possible, window sills in south-facing windows are best! Some traps will die back once first place in full sun but your plant will quickly grow more and thank you later! 

The Venus Flytrap likes a lot of water. It's best to keep in a saucer with a little standing water so they never dry out. This will also raise the humidity around them, which they love! Using distilled, reverse osmosis or rain water is best. 

Venus Flytraps love humidity. Sprits them with water every once in a while! 

Average comfortable room temperatures will be sufficient!

Venus Flytraps typically do not need to be fertilized! They eat their food! If you notice your trap isn't catching any critters (lucky for you to have a bug free household), you can place bugs in traps. Those pesky flies you find outside will do the trick!  

Browning and die-back of traps is totally normal! Prune these off and your plant will sprout new, beautiful traps. 

For division, the plants are best divided in late winter to early summer. Offshoots are cut off the original plant, but one must make sure that the piece to be cut off has its own root system. Place divided part into separate container and voila!