You got me!

What code are you working with, what material, etc.?

R could stand for "reject" or "round" or "root" or anything you want to list without any other information provided.

It's like my wife asking me, "Did you like that color?" while I'm driving down the interstate.

When I ask her, "What?"

She replies, "You weren't listening. We were talking about it last night!"

Gotta go, I have to paint something blue. I don't know what, but she must have told me about it last night.

Best regards - Al

Well, there is no such thing as a brief tutorial on them. It is also something that can't be broken out by itself as a lack of understanding of part if it is a lack of all of it.

Class R is intended for tubular TKY connections where UT is used as an alternate to RT. D1.1 does a pretty poor job of explaining it in my opinion, however; API RP2X 04 does a fair job of explaining the details. If you get a copy of RP2X (In annex S s2 introduction you'll read that it specifically references RP2X) your going to note that many of the figures found in D1.1 match those of RP2X. I've not been able to figure out which came first. You'll note under 6.13.3.1 of D1.1 that the amplitude criteria normally used for D1.1 is modified, and further, it goes into commenting on flaw characterization. Therein is the rub of it all. The standard methods for UT D1.1 style just went out the window. Whereas a specific amplitude is required for acceptance or rejection and a length only, characterizing spherical and planar root fill or cap, and as the last sentence of 6.13.3.1 states, if it's root connected, it kicks back to Class X fitness for service. (Note in annex S.8 that information in regards characterizing is given. Whereas in the main body of section 6 it's mentioning specific criteria for pores, planars etc, How are you going to judge that without characterizing the flaws, yet annex S is non-mandatory as of 06.)

6.27.3.2 Sensitivity Calibration. Standard sensitivity
for examination of production welds using amplitude
techniques shall be: basic sensitivity + distant amplitude
correction + transfer correction.

Your sensitivity is basic, + DAC + transfer correction. Class R and Class X is where the technician really needs to be familiar with ASME style UT and AWS style as it is effectively a marriage of the two. Where on class R your kicked to Figure 6.7 (figure 6.8 for root indications) you will note that it refers to a DRL and SSL (disregard level and standard sensitivity level) everything is tied to the sensitivity level as defined in 6.27.3.2

Your also going to need to profile your beam on a vertical and horizontal plane. The horizontal plane is typically performed with the 20 db drop method which is also tied into beam spread and transfer correction along with your standard index point etc checks. You cannot properly set your sensitivity without these matters being accounted for.

Now, assuming all the ducks are in a row, your tech is good to go with procedure and has been qualified in it's use, you can then judge the production flaws.
Use figure 6.7 for everything except root area flaws. Figure 6.7 is fairly easy to read but you'll note for root area flaws, it's different (figure 6.8)

They are all a product of length x height continuous or broken, diameter of the tube/pipe (D) and the thickness (Tw) of the weld. (the LH ratio is why the 20db beam profile check)
Once you take that into consideration, it should be easy enough to understand from there.

Note: Discontinuities that are within H or tw/6 of the
outside surface shall be sized as if extending to the
surface of the weld.

Do be careful of that note. If your H was 1/2" and it's top dimension was 3/8" from the outside surface, then the resulting H value would be 7/8" of an inch rather than 1/2".
If the discontinuity H dimension exceeds the value of 1/6 T then the nearest surface is drawn in and included as H.

Dunno if this helps you, but there it is.

Regards,
Gerald