1) There are other dimensions/universes which are not so much separated from ours by conventional physical space as they are by something else. Think for example of the light spectrum. The visible light you can see is only one part of the spectrum; IR and UV light also exist at the same place and time, but are not visible to you.

2) It is possible for doorways, portals, or 'rips' to occur which allow passage of beings (and possibly even other things like rocks or plants) from one dimension to another. These may sometimes occur naturally, accidentally, or they may be created.

On to elves and other mythical beings, I see two possiblities:

1) There used to be (or possibly still is) a stable doorway between our universe and theirs, and periodically they come through into our world for reasons unknown. Sometimes humans see them, and perhaps sometimes they interact with humans deliberately. As we acquire technology and become more advanced, they become more afraid of us and conceal themselves. Or, the doorway closed at some point and that's why we don't see them any more. Said doorway could be natural or they could have created it.

2) At some time in the past, a group of elves passed into our world accidentally. Not able to find a way back, they settled and were a large enough group to reproduce and survive, for a while, after which the increasing human population probably caused their extinction.

Note that this same theory works equally well for dragons, dwarves, unicorns, goblins, faerie, brownies, Bigfoot, some 'alien' encounters, ghosts, and UFOs, and may even (in my opinion) explain some Fortean phenomena such as rains of blood, mysterious disappearances of people, and alien animals (think black panthers in England or chupacabras).