The linguistic procedure outlined below is the one that can be used to make new words out of verbs, and anyone who understands English will immediately have a sense of the meaning of the new word as the sort of thing/person that does what the verb means:
What is this process called?
Nominalization is the process of how a verb or adjective can be used as a noun through applying affixes. Generally suffixes like -ion, -ment, and -er can turn verbs into nouns.
Wikipedia gives:
In linguistics, nominalization or nominalisation is the use of a word that is not a noun (e.g., a verb, an adjective or an adverb) as a noun, or as the head of a noun phrase. This change in functional category can occur through morphological transformation, but it does not always. Nominalization can refer, for instance, to the process of producing a noun from another part of speech by adding a derivational affix (e.g., the noun legalization from the verb legalize),1 but it can also refer to the complex noun that is formed as a result.2
Nominalization is also known as "nouning".
The last one sounds like verbing.
This related question sheds light on some general "rules" for nominalization.
More about agent nouns which mean "one who [verbs]" and the agentive suffixes -er and -or include with examples:
An AGENT (< agere, actus) is a person “doing” something—here, performing whatever action is expressed in the verb base.
"to travel" => "traveller" "to rule" => "ruler" "to direct" => "director"
In Middle and Modern English, agent nouns derived from verbs are almost always constructed using the agentive suffix -er (from German), less commonly from -or (from French).
There are other suffixes that will result in other kinds of nouns, like -ion usually being a thing or substantive made as a result of the verb (i.e. vacate, vacation, coerce, coercion).
In a comment, @John Lawler added, with my thanks and in the interest of saving this:
This -er derivational suffix (there's also an inflectional suffix -er for the comparative) is called the Agentive suffix. It comes from Proto-Indo-European suffix -ter/-tor with the same meaning. So we have tons of words like auditor 'one who hears', censor 'one who assesses', dictator 'one who orders' coming already formed from Latin. It wasn't hard to apply it to French and English.
