I think Ron and Stuart have done a good job there, but I'll summarize:
The word "cost" (or "costs") can be either a noun or a verb.
When cost / costs is a noun, then "cost" is singular and "costS" is plural.
When cost / costs is a verb, then "costS" is singular and "cost" is plural.
So that's probably part of your confusion right there - you have to know first whether you're talking about a noun or a verb. (As a general rule, you add an "s" to make a noun plural, but you remove the "s" to make a verb plural.)
In the OG problem given in the other post, we have "the cost(s)," so the word is a noun. Therefore "cost" is singular and "costs" is plural. The verb that matches with this noun is "are," which is plural, so we need to use "the costs... are..."
In the example "this mistake cost him his job," as another poster pointed out in the other thread, "cost" is used in the past-tense here. The past-tense form is the same whether the noun is singular or plural:
Yesterday, a big mistake cost him his job.
Yesterday, several mistakes cost him his job.
If you want to re-write the sentence in present tense (which will sound kind of funny, so let's change it and pretend we're listening to the French Open tennis tournament on the radio right now and the commentators are giving a play-by-play):
Oh, he hits the ball into the net and that mistake costs him the match!
Oh, he keeps hitting the ball into the net and those mistakes cost him the match!
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