Learn Finnish: Me emme ui täällä.

uida is a Type 2 verb, which means it ends in -da or -dä. To find the stem for negative sentences, you just remove the -da. This leaves us with ui. In a negative sentence, the main verb doesn't get a personal ending, so it stays exactly like this: Me emme ui.

Why is the word for "not" emme here?

In Finnish, "not" behaves like a verb and changes depending on who is acting. Since the subject is Me (we), the negative verb takes the "we" ending -mme, making it emme.

Could I drop the word Me and just say "Emme ui täällä"?

Yes, you can! Because the negative verb emme already clearly shows that "we" are the ones not swimming, the pronoun Me is optional.

I've learned that "here" can also be tässä. Why is it täällä in this sentence?

Both mean "here", but they are used slightly differently. tässä usually refers to a very specific, tight spot. täällä refers to a broader, more general area. Since swimming usually happens in a larger space like a lake or pool, täällä is the natural choice.