Alternative to above is to buy blank newspaper rolls. One will last you ages. Either cut into sheets about 40" long or you could make a box to protect the roll and just lift out 40" at a time. Pin each sheet to some sort of make-shift wooden frame. Choose a calm day! Use a felt-tip pen to make a central aiming mark and shoot it using some form of rest. It could be from a rifle bench rest or just something like a stick (like a bean-stick or length of bamboo), that you can steady the gun with. You'd be surprized how easy it is to aim off.

You can do one of 2 things. You can shoot at about 20 yards unsupported, just up, aim and fire 3 quick shots from one barrel over the top of each other and look for the centre of density. That will point to aiming issues, such as badly fitted barrels, sights or choke tubes.

If you want to evaluate loads and compare, shoot once at 40 yards and set up another sheet. Label each sheet according to the load, the choke, barrel etc. Back home you should be able to judge where the centre of density is. I use a plastic compass that has a point on one end of the folding legs. The other end holds a felt pen. Set the felt pen at 15" radius so it will leave a 30" circle. You can do a dummy pass and see if it is going to enclose the pattern evenly. If so, next run use the felt pen and mark it. Note with a dot where the point went. Now mark out a 20" concentric circle inside the 40. Now use a yard-stick to draw in a vertical and horizontal line through the centre point. You now have 8 roughly same sized compartments. Count the pellets in each compartment, circle each one with the felt pen and write this total boldly in each compartment. You can also record these totals in a set order so you can refer to them later. What does this tell you...

1) If you gun shoots high, low, left or right and by how much.
2) The actual choke % inside the 30" circle.
3) If it's a good long range load, (good 20" centre density).
4) If your gun likes that load, pellet size, shot type. For instance, is it evenly filled out - how many small circles can you draw that will have no pellets in them, inside the large circles, that a bird or target could fly through.
5) It will also tell you something about the effect of wind, if you note that when you shoot. Pellets do get blown off centre.
6) It will tell you if a certain wads shoots a more even pattern, or if that special type of shot is worth paying extra for.
7) Is that expensive choke tube any better?
and so on.

I suggest that, if you're not there to find out how much recoil you can tolerate, then get a strap on shooter's shoulder pad to soak it up. This is especially so if you're looking at magnum loads.

I've patterned a lot of shotguns. My 10 gauge was the most interesting and I could judge the effect that lengthening the forcing cone had, the changed choke tube, using lead, copper plated and nickel plated shot and different wads and buffers.

If you have a gun that just doesn't shoot well, this may be the only way to find out, did they make a bad one? Or is it just you?

Last advice; DON'T use steel shot on a steel patterning plate.