These days the camera can give a pretty good level of exposure feedback to the photographer from the histogram display on the back of the camer a -quick look and a photographer can check the exposure. They are likely to take repeat shots or even a small burst of photos for some situations. For example group shots they might do a couple of times to ensure that everyone has their eyes open, a few shots helps ensure that everyone should have them open at some point and gives the photographer eyes to work with from the person if they have them shut for one shot.
A few other things can also help:
1) External light meters which give exposure info based upon ambient light instead of reflected (they read the light present in the scene as opposed to the camera meter which reads light reflected off the subject). For a situation where the light is nearly or fully static this can help get solid exposures each and every time that won't be "fooled" by the subject as the built in camera meter can be*
2) Test shots and a meeting before the event - checking out the lighting of the venue can help a lot, they'll know (within a little) what to expect and where. OF course experience working within a certain area also gives this over time as well.
3) Experience - I'll say it again, experience helps a lot. Some will still take shots and bracketed exposures and the like for insurance (and since its digital it costs you nothing**). Better to have and not need than to not have and need
*good example of this is snow, which a camera will attempt to render as grey instead of white where its the dominant element in the scene under the meter.
** digital photos do cost "time" to process for the photographer. Clearly if they are shooting vast amounts of waste shots then that can slow their processing step and also might increase the size of storage space that they'll need to keep the photos on both at their place of work and also on the day shooting.