The LHC is a big ring around which particles travel at high speed and, from time to time, collide with one another.
Given that the particles were not travelling around the ring 100 years ago, and will probably no longer be travelling around the ring 100 years from now, there needs to be a way of getting them in and out.
In (INJECT): beams of particles (travelling rapidly but in a straight line) are produced by other accelerators and then diverted into the LHC ring.
Out (DUMP): the particles are diverted out of the LHC ring, the exiting beam is spread out using electromagnets, and it is sent into a big block of graphite encased in concrete.
I don't know, I'm afraid. According to the Wikipedia page on the LHC, though, injection takes "several minutes", acceleration after that takes "20 minutes", and then the beams circulate for 5-24 hours while the detectors watch for products of collisions. (Beams plural because the LHC has two beams circulating in opposite directions.)