Hatchlings and juveniles should be fed every day, it's best to feed in the evenings or at night. Once they get older, they'll start eating a bit less often. Such as when they're sub-adults around 8-12 months they should start eating every other day. Adults over a year old should be fed every 2-3 days, depending on your gecko.
Leopard geckos are crepuscular, they're most active at dawn & dusk. If you want to handle them it's best to handle them at night when they are awake and are active. As for how often, every gecko is different. Most leopard geckos are skittish when they are young, but they become more docile when they get older. Also remember that leopard geckos tolerate handling, they don't exactly like it, nor do they like being cuddled or play dress-up. So only handle your gecko enough to not get it stressed out.
When you get a new gecko, it's best to leave the gecko alone until the gecko stops running away when you approach the tank or when you go feed it. Once the initial acclimation part is over, and the gecko gets used to you as the food person, you can then start to hold the gecko more.
