There are two easy ways, one narrative and one dungeon-structural.
The easy narrative method is to skip the "finding the interesting place" part of the game with a quick narration. Something like:
You enter the Grey Portal and quickly make your way through the echoing, dripping tunnels. Cries of surprised terror and threatening growls pierce the silence occasionally, but you meet nothing more dangerous than the rats that infest this section of the dungeon. The markings on the map to the Lost Library lead you true, and soon you find yourself at the threshold of the Library—a stone arch carved with leering gargoyles and mad scholars. The real test of your mettle begins…
The advantage of this method is that it works for any dungeon without modification, and if well-presented the players will enjoy getting right to the meat of the adventure. The return to the surface can be similarly narrated, although if you want some danger between the "starting" point of the adventure and the surface, there can always be another encounter (randomly checked for, or placed) in a location, connected by similar narration.
Another advantage of this approach is that you can explore interesting parts of a megadungeon while preserving the feeling of vast underground passages.
The easy structural method is to construct or modify the megadungeon such that there are many entrances, with one entrance conveniently leading directly to the area of the dungeon in which you want to adventure. This also breaks up the dungeon into slightly more digestible sections based on proximity to a known entrance, yet players will find particular joy in discovering the in-dungeon connections between places they know. Finding a new entrance to the dungeon becomes a treasure in itself, as it offers access to heretofore unknown sections of the vast underground.
The advantage to this is that you don't need your players to buy in to glossing over movement in the dungeon with GM fiat-by-narration, and makes it easier make the exploration (legitimately) feel more in the hands of the players. There is also precedent for megadungeons built this way—Gygax's dungeons were known to have very many entrances, not all ever discovered by his players.