Balancing is a great win/win situation. The money you invest gets paid back in terms of longer engine life and greater engine efficiency. That means more power and better fuel mileage. You get to have your cake and eat it too. Balancing the moving pieces/parts mean that they move equally in and out, round and round. No one part is heavier and causing vibration and stress. (Longer engine life) It also means that you don't sacrifice power to lost motion - parts fighting against each other because they're not equal. (Better efficiency)
Balancing makes each part equal in weight to its buddies. How this is accomplished depends on the part:
Crankshaft: Weight can be removed or added to the counterweights. Removed by drilling; added by drilling and filling with heavy metal. The harmonic balancer and the flywheel/flexplate are usually balanced as a group with he crank. If you have a manual trans, this will also include the pressure plate.
Rods: Balanced to the lightest rod in the group. Weight is removed by grinding material off the top and/or bottom of the rod. The goal here is to make the rods equal in weight and to also balance them top to bottom. Sorta like a throwing knife.
Pistons: Like the rods, they're also balanced to the lightest guy in the group. This also takes into account the weight of the rings. You'll be asked to bring one set with the pistons. Weight is removed by removing metal from the bottom of the piston pin bushing, and sometimes from the underside of the crown.
The actual cost is determined by how close to '0 balance' you go. Your machinist will give you a range of weight and cost. My machinist balances to within 1 gram and charges $225 for a V-8 engine. A gram is equal to about half a sheet of notebook paper. That's pretty close! Done well by someone that knows their craft, you end up with a motor that's noticeably smoother throughout its entire RPM range. Your butt-dyno and your wallet will also notice the difference!
Blueprinting is using machine procedures to make the pieces/parts dimensionally exactly like the engineers designed them. No tolerances, no slop, everything fits perfectly and functions as dreamed. On the extreme side, blueprinting involves every piece of the engine. From an affordable point, you're mostly interested in the cylinder bores being parallel with each other and perpendicular to the crank (Align bore). You want to make sure that the crankshaft bores are all aligned and perfectly straight (align bore). You'll also want the block surface to be exactly perpendicular to the bores, parallel to the crank and perfectly even (decking). Cylinder heads get the same surface treatment.