Learn Danish: Hun finder altid på gode ideer. - She always comes up with good ideas.

By itself, finder means "finds." But finder på is a phrasal verb meaning "to come up with," "to think of," or "to invent" (like an idea, a story, or an excuse).

Why does altid go between finder and på instead of before the verb?

In Danish main clauses, the verb must come in the second position (the V2 rule), and central adverbs like altid (always) immediately follow that first verb. This naturally forces the adverb to split the main verb (finder) from its preposition (på).

Could I use opfinder to say she "invents" good ideas?

Not naturally in this context. Opfinder is used for inventing physical things or major scientific concepts, like the telephone or a new technology. When referring to coming up with mental creations like ideas, excuses, or games on the spot, finder på is the right choice.

I sometimes see idéer written with an accent mark. Is ideer without the accent also correct?

Yes, both are completely correct in modern Danish. You can write the singular as either idé or ide, and the plural as idéer or ideer. The accent simply reminds readers that the stress falls on the final syllable, but using it is entirely optional.