Every adoption is treated as an individual case, so while the process normally takes about a week, it can be shorter or longer depending on a number of factors, and this should not be taken as a guarantee.
Centre staff will do their best to find a dog whose needs suit your circumstances from the start, so many people agree a match with centre staff on the first visit and are able to take home the dog soon afterwards (pending a home check).
Some might need to visit a centre more times to find a suitable dog, and occasionally dogs might need to get to know their new owners more gradually, over several visits.
Whenever you discuss a dog with centre staff, their needs will be explained to you so that you know what to expect.
If you know there is a big event (moving house, going on holiday, a new baby) coming up soon, it's best to start the process after everything has settled down, so that whenever you find your new dog, you're ready for them.