Learn Danish: Lærerne presser på for højere løn. - The teachers are pushing for higher pay.

The phrase at presse på is a phrasal verb meaning "to push", "to urge", or "to exert pressure". If you just used presser, it would sound like physical squeezing or pressing, such as pressing a button or squeezing juice from a lemon.

I sometimes mix up the spelling of "the teacher" and "the teachers". How can I tell lærerne is plural?

Lærerne is the definite plural ("the teachers"). For nouns ending in -er, the definite singular adds -en to make læreren. However, for the definite plural, instead of adding -ene to the plural form (lærere), Danish drops an e to make it easier to say, resulting in lærerne.

Does at presse på always take the preposition for?

When it means "pushing for a specific outcome", yes, it usually takes for followed by a noun, like højere løn. However, if you are pushing for an action to happen, you would use for at followed by an infinitive verb: De presser på for at få en aftale (They are pushing to get a deal).

Why doesn't the adjective højere change its ending to match the noun løn?

Højere is a comparative adjective ("higher"). In Danish, comparative adjectives (which typically end in -ere or -re) are completely fixed. They never change their endings to agree with the gender or number of the noun they describe.