In dimorphic species of birds, there are visual differences between males and females (e.g Eclectus), sexing them will be easy. However, in other species there may be minute differences between sexes, your vet will be able to give you a reasonably reliable indication as to gender based on visual assessment and physical examination. But this is not as accurate as DNA sexing.
If your bird is of a species where gender is not obvious, a small drop of blood can be taken for DNA testing to determine gender. In some cases, e.g. with breeding birds, your vet may suggest surgical sexing under anaesthesia using a rigid endoscope so that the reproductive tract may be assessed at the same time as determining sex. Ask a staff member if you would like your bird DNA sexed.