Okay, so here is how it all works. Basically, I just watch the edited English version simultaneously with the unedited Japanese version, and note all physical differences, and the important dialogue differences. Changes are noted as follows:

Cut
Cuts are, essentially, the full removal of footage. Whether it be the snipping of a few frames, or a few minutes worth of material, I note them all in these boxes.
Alteration
Alterations are all physical changes to the video, save the removal of the video itself. This includes things such as digital paint, sped-up or slowed-down animation, zoomed-in footage, or placing footage out of order. There is a ton of this, because simply removing footage would make the music skip. Such was not a problem with DBZ, as an entirely new soundtrack was used, and could be scored in time with the edits.
Dialogue
This is where I note changes in the dialogue. It will only consist of the important changes. Essentially, those are changes to the plot, or the toning down of the "naughty" lines. It is not my intention to compare entire scripts, or make fun of the stupidest lines. (Even if it were, I'm not very funny, anyway.)
Other
Well, this is the miscellaneous box. I may note things such as terminology changes that don't necessarily mess with the plot, give an opinion on something related to the episode, or note a change to the music (like the removal of an insert song). Really, just anything that doesn't fit in the other boxes.

These are the changes that are present in every episode, for reference:

Other
The opening themesong, Makafushigi Adventure!, has been dubbed into English. The instrumental arrangement is a new one, since it seems there was no karaoke available. The vocals are not TAKAHASHI Hiroki's, either; the performer(s?) are uncredited. The lyrics are not at all translations, or even close.

However, the English Makafushigi Adventure! was not used for Toonami, where the episodes predominantly aired. Toonami uses its own custom clip openings; two different ones existed for DB. The reruns on the SVES block did use the original English opening, however.
Other
The ending themesong, Romantic Ageru yo, has also been dubbed into English. The instrumental arrangement is also a new one, for probably the same reason. The vocals are also not HASHIMOTO Ushio's, and are not credited (though some said it to be Melodie Lenz, who voiced Kuririn's daughter in DBZ). The lyrics are somewhat closer than the opening, but certainly not a direct translation.

To break the pattern, the ending did appear in both the Toonami and SVES versions. But it was cut to only thirty seconds long, going from just the first line to the last line. The full version is only available on video. Full TV size version, that is.
Other
The only opening animation available to FUNimation is the first one, which was originally only used for the first 101 episodes. After that, a new animation was used from 102 until 153, featuring the newer characters, and new designs of the older ones. There were also four different endings. The first one, used in episodes 001-021, didn't have Lunch or Kuririn, but the second, used in episodes 022 to 101, did (and is the only one FUNimation has). The third, used in episodes 102 to 132, was the same as the first two, but with the additions of Tenshinhan, Jiaozi, Yajirobee, and Karin. The fourth and final ending, used in episodes 133 to 153, was completely new, with the characters in their adult, 23rd Budoukai forms. I would love to do a more detailed feature on these animations, when I get the equipment to do so.

I should like to note that it has come to my attention that the Dragon Box for DB only has "clean" versions of the first opening and the second ending: the only two FUNimation have.
Other
The eyecatches are not used on Cartoon Network at all, but they are available on the DVDs. There are two of them: one with Gokuu and Oolong, used until episode 042, and another with Gokuu and Kamesennin used from 043 until the final episode. The next episode previews are not available anywhere, however. The story is that FUNimation received them all from Toei without the audio. They were used in the DBZ dub, only because both the voices and music were redone for it. But DB used the original music, so they only could have redone the voicing.