It's kinda like asking how much it costs to build a house. It depends on what "finished" means, e.g. will it have a full bath? A half bath? Laundry room? Carpet or hardwood floors? Drywall or dropped ceiling? Windows? Does it include new stairs? Is there a dampness problem to be corrected? New HVAC?

Generally speaking, most basements can be finished for between $15 and $40 a square foot, bearing in mind that smaller basements actually cost more per square foot than larger ones because there are certain fixed costs (like a bathroom).