A degree of discomfort is likely to start with. You can expect some aching and tenderness in the gums as the teeth start to move, but this mostly wears off after a few days.
Fitting the brace should not be painful. For a fixed appliance the brackets are simply glued to the faces of the teeth; metal bands may also need to be cemented round the back teeth. No anaesthetic is needed.
As the biological processes get under way round the tooth roots to allow the teeth to move, you can expect some aching and the teeth will be tender to bite on. This usually settles down in a few days, although some patients do experience a degree of tenderness for a longer period. The amount of discomfort varies enormously from person to person. It may be helpful to take your normal painkillers or a day or two.
Some further discomfort may be experienced when the brace is adjusted subsequently, but this depends very much on what adjustments have been made.