The Game Boy version of the game, similar to the SNES and NES versions, require for the player to evade confrontation with the Wet Bandits. Similar to the SNES version, the player has to gather up various items in the game and then dump them into a laundry chute to deposit them into a safe. Sometimes, the player might resort to using the items the bandits planned to steal against them by having them dropped on their heads, as well as instigate certain traps à la the movie (e.g. dropping a paint can on their heads). There are four levels in all, each taking place in a different area of the house, as well as each having a different item that the player must recover: The first level is stuff pertaining to jewelry/gold/silver items, the second level has toys, the third level has various Electronics, and the fourth level has various exotic pets that are both rare and expensive.
Source: Wikipedia, "Home Alone (video game)", available under the CC-BY-SA License.