This will depend on whether or not liposuction was part of the treatment. If it was then there will be compression for approximately 6 weeks. During that time depending on the area treated there can be increase swelling with exercise. Walking is a good start and walking up hills or on a treadmill with an incline is helpful exercise during this time.
I appreciate your question. "Normal activity" can mean different things but I generally have seen patients return to work in 3-5 days. Factors such as the areas treated and motivation play a role in this. But from a surgical standpoint I think 3-5 days is what I expect and then I still have people refrain from resuming exercise for 2 weeks.