Welcome to Guntalk-Online JD!
Target group size is generally measured from center point to center point of the two farthest hits in a shot grouping. To measure this distance, first measure the outside edges of the widest two hits, then subtract the caliber (diameter) of one of the bullets from the total measured distance. This will give you the approximate center-to-center distance. I say approximate because the holes in the target are not the true diameter of the bullet. They are actually smaller. The paper stretches when the bullet hits it, and only a small portion blows out, then the paper shrinks back around the hole as the bullet passes through. So if you really want to get the actual group size, you subtract the measured dimension of the target's visual bullet hole from the total distance measurement.
Scoring is accomplished by measuring the actual diameter of the bullet hole in the target. To do this a competitor typically uses a transparent plastic template called an overlay.
The overlay has various bullet caliber diameters on it. One can center the diameter of the bullet caliber shot over the target hole and see the actual size of the bullet on the target - the template marking will be bigger than the visible hole. If a shot (actual diameter) touches the edge of a higher scoring ring, the shot is scored at the higher value. The higher value is determined if the black line on the template overlay touches the white line of the scoring ring (aiming black rings) or if the black line of the template touches the black line of the scoring ring for the (white rings - non-aiming black) target ring values.
There can also be a shot that traverses two or more lines - this is typically referred to as a skidding shot or a skidder. A skidder occurs in a match where turning targets are utilized and must be an entry hole into the front face of the target. An exit hole is not a skidder - it's a miss. A skidder is scored differently based on if the shot hits into the target towards the higher value rings or if the shot is traveling away from the higher value scoring rings. Toward the higher value and the score is the value one ring higher than the initial entry point. Away from the higher values and the shot is recorded at the value of the initial entry point.
One can also use a device called a scoring plug. But in competition, only a match official can insert a plug into a target. Then the two (shooter & scorekeeper) must agree on the shot's value. If they cannot agree, the target is pulled from the frame, with the scoring plug still inserted, and sent to a match official to determine the shot's value. This is called a challenge. The shooter must initiate the "challenge" and declare what the challenge is for - either "number of hits" or "shot value." Typically the shooter must place some pre-established monetary amount on the target to challenge. If the shooter wins the challenge, he/she gets their money back. If the shooter loses the challenge the money if forfeited to the match. This way folks do not arbitrarily challenge scoring because it has a monetary worth to them and the matches flow more smoothly. (see this link to learn more on using scoring gauges "plugs"
http://www.odcmp.org/0108/ScoringGauges.asp )
Scoring values are as typically as marked on the target. However some targets have an "X" ring. This ring holds the highest numerical value of the rings on the target. Usually this is the number ten. Therefore if a shooter fires ten shots in a string and has three shots in the X ring, six in the ten ring, and one in the nine ring, his score for the total string is a 99-3x. The X's are valued as tens but they are recorded at the end as a separate number for tie-breaking identical numerical value shots. For example: two shooters fire strings of 99 but one has 5x's and another has 4x's, the lower X shooter lost the string to the higher X count shooter.
MOA- is approximately 1" at 100 yards. This is the actual angular measurement of a compass degree in sixty equal parts called "minutes". At 200 yds an MOA is ~2", 300yds ~ 3", etc. Measuring the MOA for shooting is from the outer edges (minus the bullet hole diameter) of the two most distant shots in a group. It is not from a imaginary center point of the shot grouping.
Hope this helps.
R,
Bullseye