Verb Nominalization

How are verbs nominalized in the following sense: run-runner(s), teach-teacher(s), slay-slayer, read-readers, swim-swimmers, sing-singer, paint-painter, ect. Examples:
The runners were tired.
The singer was drunk.
The readers are angry.
Thank You.

Suffixes like 者, 家, 手, etc.

走る -- 走者 (not sure how common this one is; it may be a combination like 競走選手 or something)
歌う -- 歌手
読む -- 読者
科学 (granted, not a verb) -- 科学者
民主主義 (again, not a verb) -- 民主主義者
専門 (pattern, here) -- 専門家

In addition;

走る[hashiru] - ランナー[rannā] / 走者[sōsha]
教える[oshieru] - 先生[sensei] / 教師[kyōshi]
殺す[korosu] - 殺人犯[satsujinhan] / 殺人者[satsujinsha] / 殺害者[satsugaisha] / 殺し屋[koroshiya]
読む[yomu] - 読者[dokusha]
泳ぐ[oyogu] - スイマー[suimā] / 水泳選手[suieisenshu] / 泳者[eisha]
歌う[utau] - 歌手[kashu] / シンガー[shingā]
描く[egaku] - 画家[gaka]

There are many words that are more commonly used than the "verb root + suffix" form depending on the verb.
The Plural and singular are the same in most cases in Japanese.

Thank You. I will look them up.