As a long time fan, I'm familiar with the tell tale sound effects that indicate when the beaming process is taking place. What do residents of the Star Trek universe witness from the ground when people beam back to or down from the ship?
The only tell-tale is the distinctive audio warble that accompanies both the materialization and de-materialization. Memory alpha has a lengthy entry on the transporter here. In addition there are several episode where the characters have a reaction shot when someone beams into their presence even when they are expecting their arrival.
There is also at least 2 examples of characters recognizing the sound of a transport in process and jumping into the beam with the intended target, i.e. the Romulan commander in "The Enterprise Incident" and Gillian in "The Voyage Home"
So, what you would witness is, 1) The sound of impending transport and then 2) The fade in (or out) of whoever or whatever is being transported. Just my opinion I tend to think of the sound as a sort of "heads up" that a transport is about to happen like the back up beeper that some cars and trucks are equipped with.
On a side note, the Klingon transporters shown in the episode "Day of the Dove" were completely silent.