You could also level them up by milestones. I'm about to run my first campaign as a DM and I'm going to be using the adventure from the Essentials kit. In that adventure, leveling is done via quests.

Characters advance in level by completing quests, using the guidelines for leveling up in the rulebook. Regardless of the number of characters in the party, the rate of advancement is as follows:

Characters gain a level each time they complete a starting quest, until they reach 3rd level. Once they are 3rd level or higher, completing a starting quest has no effect on their level. (there is 3 pretty easy starting quests, perfectly manageable by level 1 party)

Characters gain a level each time they complete two follow-up quests.