As is frequently the case in woodworking, it depends.
Most common wood glues, including all PVA-type adhesives (both white and yellow), dry by dehydration. That is they are literally dried, principally by the wood absorbing moisture from the glue and a little by evaporation.
So clearly there will be two main factors affecting drying time — the moisture content of the wood and the local conditions (temp and humidity). So in short, if the wood is dry and it's warm drying times are shorter than if the wood is less dry and it's cool.
Because of this it's only possible to give very general guidelines as to drying times and glue manufacturers will provide conservative estimates so people don't get themselves into trouble.
how long does the workpiece need to remain clamped before I can remove the clamps and move on to the next stage?
In the right conditions a glue joint can be dry enough to take movement and light handling (no more than this!) in 20-30 minutes but when it's cooler this could take an hour or longer.
Err on the side of caution, because if you take the clamps off too early the glue joints can open up very slightly and result in greatly reduced strength in the joint. Because of the high humidity and lower temps that are common where I am I don't take clamps off for at least two hours and as much as possible leave them of for the complete drying time, which in my case is 6-8 hours or overnight if the piece was completed late in the day.
It's important to note that with most glues low temperatures can retard drying greatly and if low enough may prevent the glue bonding properly. So do heed any on-pack instructions with regard to acceptable temperature ranges or you could end up with a piece that isn't bonded together properly even after the temperature has subsequently risen.