The process is called "agentive nominalisation", and the resulting noun an "agent noun".
From what I've seen most languages with the concept of agent noun do it like English does: start with the verb, remove any potential verb-exclusive affix, add a specific affix for agent nouns. That seems to hold true even for non-IE languages; see Old Tupi and Cebuano. However there are plenty twists you can add to that, for the sake of conlanging:
- It doesn't need to be after the root. A prefix, infix, or circumfix is fine too.
- You could have multiple affixes instead, either for different semantic purposes or different phonetic environments. (I think Irish does the later.)
- As typical for affixes they can also interact with the root; for example Old Tupi does this, if you plop that -sar (agent noun former) into the verb aûsub "to love", the result is not *aûsubsar as you'd expect, but aûsupara (I think /bs/→/p/?)
- Something akin to Arabic vowel alternations seems realistic IMO. Or even consonant mutations.
- Instead of an affix, a separated word. It would be like saying "drive doer" in English, instead of "driver".