Search forms handling of plurals
You can certainly achieve a very rudimentary form of plural search by following the recommendations in AbbeyDesign's answer.

However, it comes with an important caveat: it won't work for plurals which do not include the singular form.

For example, baby / babies, knife / knives, or tooth / teeth.

If you need to accommodate this requirement, Craft's built-in search probably isn't going to cut it, and you'll need to go with something a bit more sophisticated.

I haven't personally tried it, but I think Search Plus can handle this. It's basically a convenient wrapper around Algolia, a very sophisticated search tool, which automatically handles pluralisation.