Mary saw an angel at the Annunciation.
St. Joseph, Job, Jacob, Laban, the Wise Men, and whoever else, however, were visited by angels in their dreams.
Tobias was joined by the angel Raphael in his travels-- in disguise.
So those are the three ways we usually encounter.
People who encounter an angel face-to-face happen, but are extremely rare. Padre Pio would be one example of this kind of person. I know two people who have seen the angel that guards my old church, although I’ve only spoken to one of them. That person didn’t really have words to describe it, just that it was “big”.
People who are visited by angels in their sleep are going to be much more common. The angel has a message, but the person, for whatever reason, is not given the privilege of actually seeing them physically. A lot of times, you don’t actually see anything, even in your dream, but you hear.
People who are visited by angels in disguise usually happen in emergency situations. You’ve heard all the disappearing-stranger stories. So even though they’re immaterial, they’re allowed by God to take a certain guise to accomplish their work in the physical world.