Some clubs and fine gunmakers use "Great Iron Plates" smeared with white grease paint to shoot patterns.  This has the advantage that there are no "consumables" except for the ammo.  Take a shot, examine the result, repaint the plate and shoot again.  It has the disadvantage of only allowing you to look at one pattern at a time and it requires that you fix any problems right then, while you're at the range.

Other systems use paper targets of various sorts.  Some targets are covered with printing which simplifies your later analysis.  Others are blank.  In some cases the standard 30 inch target circle is drawn before you shoot and you count what fell inside.  For other methods the center of the pattern is estimated and the 30 inch circle is drawn around the center after you shoot.  Some methods recommend a plastic disk which covers the center of the pattern (which is assumed to be OK) leaving the pattern tester to count only the holes in the outer part of the 30 inch circle.  In any case, there is a lot of  BB hole counting involved.

Whether you shoot at iron or paper, you carefully measure your distance to the target, point toward the center of the pattern target and fire your gun.  Repeat as necessary.  To gain the most from this shooting, you need to have some idea or a plan as to what you are trying to gain from these patterning shots.  Where you stand and the loads you use are very different for Skeet than for long yardage Trap shooting.  You should simulate as closely as possible the conditions you expect in the field.

Links from this page describe several situations which can give you ideas about how you might want to do patterning.  One addresses showing a new shooter how a shotgun behaves.  Another talks about how to determine if shot quality really matters for Skeet shooting.  Another covers a case of a trap shooter trying to soften his load to avoid flinching.  Finally, there's a discription of a technique to optimize your pattern for a specific kind of game, specifically pheasant.

The ShotScan® patterning system uses large heavy weight paper targets with a center pointing spot (someone said you don't aim shotguns).  You take the shots, we do the counting.  Our  analysis of your pattern is based on the pattern center we calculate after you shoot.  We tell you how far from the pointing spot you were just in case that's where you pointed your gun.

The ShotScan® patterning system also includes a booklet called "Planning, Writing and Shooting" which should help you focus on goals for your patterning work.  The Sales page has all the details for how to order and proceed with ShotScan® pattern analysis.