in terms of spelling, you still need to learn supplementary rules to actually complete all the inflections. So how regular is that?

I ran into this in Spanish classes and I object. A Spanish example might be something like buscar which has forms like busque, but that's just a spelling convention to retain the [k] sound when the c would be sounded like an s or a th due to the following vowel.

The terms regular and irregular were preceded by the terms weak and strong respectively. The past tense of the weak verbs involved a suffix that included a d or a t, at least in the singular. The mark of a strong verb was a change in the root vowel sound, a process known as ablaut. Note that some of the weak verbs also had a vowel change, but it was due to other things than what is strictly known as ablaut. Examples of these weak verbs would include teach, taught and think, thought. Probably these qualify as irregular verbs today but they were considered weak in OE.

On the other hand, would a verb like put, which doesn't change at all, be considered regular (how much more regular can you get?) or irregular (it doesn't follow the regular root, rooted, have rooted rule)?