Learn Finnish: Älä koske katkaisimeen likaisilla käsillä! - Do not touch the light switch with dirty hands!

It is derived from the verb katkaista, which means to cut, snap, or turn off. By removing the infinitive ending and adding the instrument suffix -in, we get katkaisin. Literally, it describes a tool used for breaking a circuit or cutting the power.

Why does katkaisin turn into katkaisimeen here?

Nouns ending in the instrument suffix -in change to an -ime- stem before adding most case endings. Because this sentence requires the illative case (the 'into' case), we take the stem katkaisime- and add the illative ending -en, resulting in katkaisimeen.

Why is the switch in the illative case (katkaisimeen) rather than the partitive or object case?

The verb koskea (to touch) always requires its target to be in the illative case. In Finnish, you do not simply touch a thing; you always touch 'into' a thing.

The English translation says 'with dirty hands'. Why doesn't the sentence use the word kanssa (with)?

When 'with' indicates the tool or body part used to perform an action, Finnish uses the adessive case (-lla/-llä), which we see here in likaisilla käsillä. Using kanssa would imply accompaniment, making it sound like you and the dirty hands are touching the switch together as companions.