This is a very vague question. Do you have a specific time period or region in mind? Depending on the area or technology of the time you can get a million different answers for this question. The general definition of a siege would be for the attacking army to encircle the defenders and cut off all supplies. Depending on how many supplies an army has a siege could last anywhere from days to months to even years. More information would be required for any one to give you an accurate answer to this question though.