DHIA is hard at first because it's really tedious. There are many small details that blur together while you are trying to figure it out. Ask a lot of questions. Unfortunately, that's the best way to get started.
Do you want to do most of the work yourself (owner sampler), trade working for other herds who work for you (group), or pay someone (possibly a neighbor in cookies) to do most of the work (standard)? Do you care if you don't get genetic evaluations the first year you are on test (Owner Sampler doesn't get an evaluation the first year on test)? Are you at risk of being on the Top Ten list (Owner Sampler doesn't qualify for top ten, and you would need an extra verification test for other types)? Do you want to work with paper forms, or enter your test data on a PC? Do you want to keep costs as low as possible, or can you pay a bit more for more convenience? Do you care about being able to order disease or pregnancy testing from your lab, or if you can get MUN (which can tell you about your feeding program)? Those will give some insight into which test type and DHIA you should choose.
You need to pick a lab/Dairy Herd Improvement Association to send your milk to. Most of us use the one closest to us, but you don't need to. The lab will deal with the "nuts and bolts of testing" and some have slightly different requirements. http://www.dhia.org/members.asp This is most, but not all of the labs. The one I use is not on there. I go through Willamette DHIA which is in Salem, Oregon. They are closest to me, but I also really like them. I test for a herd that uses Washington DHIA, and have heard good things about them too. The DHIA will assign your herd number, give you the vials, certify your scale (I use this one https://www.amazon.com/American-Weigh-Scale.../dp/B0012TDR9E) and you will send in your samples to them.
The lab will have one or more data center they send your raw data to. They will extrapolate from a few samples and let you know how much your animal produces over a year. I love DRMS http://www.drms.org/ and use software called PCDart to enter and upload my test weights and animal information.
You need to decide who will do your testing. They will need to be certified by the DHIA. Some have online certification programs. I used DHIA West. http://caldairygoats.com/cdhiagoats.htm Their program is $40 and is good for two years. To sign up, you e-mail Alfred and he sends a paypal invoice. To be honest, the training isn't great, but think of it as a hoop to get through. The DHIAs don't want to fail us, they want us to understand. For that reason, don't get too upset if you aren't sure of test answers. I don't have any problem talking about what is a correct answer, and why, although I wouldn't just hand over an answer key.
Once you know what DHIA and Data Center you are going to use, and maybe your herd number, fill out ADGA's form. If you don't have your herd number yet, don't worry about it. You can send it to ADGA later. You don't actually have to sign up with ADGA and pay their fees. You can put any animal on test, registered or not. But animals with ADGA registration numbers are easier to get public information for. And if you do the rest of the steps, you may as well sign up with ADGA and get any awards, IMO. (Editors note: TMGR members sign up with Norm Geiser - see Milk Program page.)
Once you have your tester certified (who may be you, or anyone you don't own a goat with and isn't a relative), and have your vials and ladle (some DHIAs provide them, I bought one designed for salad dressing for $2 from a restaurant supply store) and forms, you are through the hard part. Roughly once a month, you milk each goat like normal. You weigh the milk each produces, and scoop a small amount of milk from each milking into a vial. If you milk twice a day, you fill the vial half full each time. If you milk once a day, you fill the vial all the way from your only milking. You can dam raise and milk test, you just need to be able to pull kids for a 24 hour period. You send your forms and samples to the lab, and you get reports back. The price varies from DHIA to DHIA. With 8 goats on test, using software instead of forms, it costs me around $30 a month, plus shipping. I just mail samples in Priority Mail boxes.
Depending on your test type, you may need a different tester to come in once a year to do a "verification test".
IMO, the "best" test type is "standard" where you have a neighbor become your tester. You get genetic evaluations the first year, and you don't need to do a verification test unless your animals are doing really, really well. After the first year, you may want to move to Owner Sampler. You will need a verification test once a year, but it can be easier than scheduling someone else to come to your farm.