Learn Finnish: Ministeri matkustaa Lontooseen avustajineen. - The minister travels to London with her assistants.

It starts with the plural stem of avustaja (assistant), which is avustaji-. Then we add the comitative ending -ne, and finally the third-person possessive suffix -en (meaning his, her, or their).

The translation says "with her assistants" (plural). How would we say "with her assistant" (singular) using this case?

It would actually look exactly the same: avustajineen. The comitative case always attaches to the plural stem of the noun, regardless of whether you mean one or many. You have to rely on context, or use the postposition kanssa (like avustajansa kanssa) if you need to be perfectly clear that there is only one.

Can I just say avustajine without the -en at the end?

No, when the comitative case is attached to a noun, it always requires a possessive suffix at the end. The -en here is the possessive suffix that points back to the minister.

Is it common to use words like avustajineen in everyday conversation?

Not really. The comitative case is quite formal and is mostly used in writing or official news reports. In everyday spoken Finnish, you would normally express this by using the postposition kanssa instead, which would be avustajiensa kanssa here.