Learn Finnish: Mökillä meidän pitää asua vesijohdotta. - At the cottage we must live without plumbing.

You start with the basic word vesijohto (water pipe / plumbing). Find the stem by putting it in the genitive case (vesijohdon), remove the -n, and add the abessive ending -tta (meaning "without"). Because you use the genitive stem, the strong "t" in johto undergoes consonant gradation and weakens to a "d" in vesijohdotta.

Could I just use the word ilman (without) here instead of the -tta ending?

Yes! In spoken Finnish, it is actually much more common to use ilman followed by the partitive case: ilman vesijohtoa. The -tta (or -ttä) abessive ending is completely correct but sounds a bit more formal or literary, though it is still widely used in many everyday set phrases.

Why is the subject meidän (our) in the genitive case rather than me (we)?

This sentence uses a necessity structure. When using the verb pitää to mean "must" or "have to", the person who has to do the action must be in the genitive case (meidän). Notice also that the verb pitää stays in the third-person singular rather than conjugating to match the subject (it doesn't become pidämme).

Why do we say mökillä (with the -llä ending) instead of using the "in" ending (-ssä)?