This is one of the subjects most frequently asked about, and honestly the one with the most answers. Different things work for everyone.
Obviously moisture is key. Especially in the winter months. How often should you moisturize? As often as you think about it. I keep hand cream in just about every room in the house, beside all the sinks, in my nightstand, in the car, in my purse etc. During the day I moisturize with whatever I grab. At night, I apply GIRLY BITS FRAZZLE FIXER CUTICLE OIL and a heavier hand cream to my hands and feet. I rotate my hand creams, and often try new things. At the moment I am really liking Gold Bond Ultimate moisturizing skin therapy cream with Aloe, Eucerin Plus intensive body cream, and Lay It On Thick by Bath and Body Works.
Regular cuticle maintenance will go a long way in encouraging healthy nails, and in making the most of what you have. I gently push my cuticles back immediately after getting out of the shower, using my thumb nail and a towel or facecloth. Then I moisturize, with CUTICLE OIL or a heavy cream.
I do not usually need to use a cuticle remover, but if you find yourself falling behing in regular maintainance and need to do some removal you can use pure dish soap. I know, I know... but you know what? It works. And I know more than a few nail techs that use that as their only cuticle remover when doing manicures. Just pour some into a nail polish bottle that you have cleaned out well with pure acetone, (and let dry overnight) and you have the perfect applicator. There is absolutely no need to traumatize your cuticles with rough removal, and please please do not be tempted to clip them. The occasional use of a cuticle nipper to get rid of a hangnail etc is ok, but if you are actually removing cuticle with them, you are causing a cycle of excessive cuticle growth, and running the risk of a nasty infection. I know it's tempting, but if you get into a regular routine, you will not need to clip them.