True patterning of a shotgun is for choke and load - it's tedious but you can learn a lot about the ammunition and choke.
Get seven 36x36 inch sheets of paper or cardboard. Draw a 15-inch circle and a 30-inch circle on the paper and make at least 5 targets. I usually make 7 targets, and this will become clearer as to why later down the post.
Select the manufacturer and shell you're going to test. For example, Winchester 2-3/4 inch 1-1/2 oz, #4 shot.
Select the choke you want to use for the load and game. This is where you'll have to make a decision. Most of the people interested in patterning shotguns are shooting clay sports games and the patterning is done at 40 yards. You'll have to decide if that's a reasonable distance for your use or not. If it is - use 40 yards. If not, adjust the distance for what you think is best.
Setup the 1st target aim at the center of the target. Shoot one shell at the target and retrieve the target and place a new target at the target holder. Evaluate whether your gun is shooting at the point-of-aim (POA) or not (low, high, left, right).
If your gun shoots to POA, then skip the next part and go directly to shooting 5 test targets. If it needs an aim correction...
Adjust your aim at the target (if needed) by the amount you think it takes to correct for the aim and shoot the second target. Retrieve the target, and evaluate that target and see if you have corrected enough by comparing with the previous target.
With two targets you should be able to figure out how much correction (if any) is required. Now shoot one shot each at the remaining 5 targets.
Take the targets home and get ready for the tedious part.
Open up one of the shotgun shells, take out the pellets and count them. This will tell you how many are loaded by the manufacturer for that shell / load. In theory, you should be able to do this by weight or have a pellet count from the manufacturer - it never works out that way - you have to count the pellets yourself.
Once you have the pellet count you can evaluate the targets. You're looking for three things: 1. number of pellets in the 15-inch circle, number of pellets in the 30-inch circle, gaps (holes) in the pattern that are large enough to miss the target.
I use a highlighter - orange for the 15-inch circle, yellow for the 30-inch circle. I highlight the pellet holes in the target as I count and then write the number in the lower right corner of the target as I finish counting each circle.
Then I take a red Sharpie marker and start evaluating the target for holes (gaps) in the pattern that are large enough to cause a miss on the target. I mark the outline of the hole - and when done, count up the holes and put the hole count under the pellet count.
This will tell you the pellet distribution with the choke and ammunition combination, how even the pellet distribution is and whether there are gaps in the pattern due to the pellets being distorted as they go through choke.
The information will take out the, "I could have sworn I aimed right at the turkey but the SOB just walked away" moments.
Your miss could be: gun isn't shooting to point of aim and/or there are holes in the pattern.
While a lot of work, tedious, and not an exercise for everyone, you can find out how chokes change the pattern, differences between brands of ammunition, and if there are repeatable problems with a specific choke / ammunition combination.