There are multiple ways of when to record the instruments of your band. None are wrong, but some sound better than others. One method of recording is to record everyone except the vocals at the same time. This will give you what people call a "live sound". Using this technique it is very difficult to manipulate since the sound from the other instruments are bleeding into your recording. This is the most simple but it also gives you the least quality recording since you can't improve on each specific part when editing.
The other, better quality, way of recording is to record each person separately. In most studios this is the preferred way because the rooms are small and dedicated to each type of instrument. The pros of recording one at a time is that they can redo a performance easily without having to deal with getting the band back in sinc. Also, now you can reap the benefits of easily editing each specific sound with every minute detail without having extraneous sound. The cons of this type of recording is it takes much longer to finish the song. Also, it might be hard for the people playing because it might be hard for them to keep in time with the rest of the band while just listening to them through headphones rather than live where there is chemistry.