Actually not much time at all. Normally after putting in the grout you have to wait no less than twenty four hours to get it wet. But make sure the grout was done correctly or you may face the problem of having to replace the shower liner if any water had got in.
It is important to follow any instructions that came with the grout. Curing times can vary. The curing process takes longer than the drying process. If you chose to damp cure then the process would take at least 72 hours. Make sure the temperature is consistent and not too cool to encourage a faster curing time.