The screen itself consists of a rectangular frame of wood or metal over which is stretched a specialized polyester fabric. This can be stretched by hand using techniques similar to stretching canvas for painting, (if anyone still paints on canvas) or specialized stretching systems can be used. Screens can also be stretched by using what are known as "retensionable" frames. Theses are frames that allow the mesh to be re-stretched between uses to insure that it is at optimal tension. It is a general understanding that, to a point, tighter screens make for higher quality prints. The tension level of a screen can be measured by a 'tension meter', a device you will find is standard equipment in most shops. The tension is measured in units called 'newtons' and 5-10 is a generally the bottom of the suitability spectrum and 20-40 is the typical upper range for conventional mesh. Wooden frames usually operate at around 7-12 once broken in and metal frames hold about 15-25. Retensionable frames usually hold about 30-40 newtons but are capable of tension levels near 100 with specialized mesh. Unfortunately the jury is still out on what the point of diminishing returns is for tension levels , but anywhere above 20 is generally acceptable, depending on the thickness of the fabric.
When you pay a "screen charge" you are paying primarily for the labor it takes to prepare and expose your image. This process is fairly involved and the $10-30 charge barely covers the expense. If a shop is using retensionable frames they will actually re-shoot the screen every time it is printed but you generally would not be charged again. In halftone work several screens often must be exposed to yield one that has no moiré patterns. It is a strange but common misconception that paying the "screen charge" means that you can take the screen home with you. This is not true.