Can someone explane to me how this cards work?

example: STUDENTS OF THE ARCANE card

After the initial setup, any time either you or your partner gains a spell (from any game effect other than this card), the oder draws a random spell from the spell deck.

Q: does this mean also when my partner buy a spell i gain spell to?

It's interesting as I manage linguists, so words really matter. Unfortunately, this is not the case for FFG's editorial staff. In the case of the word "gains" the general intent behind the use of the word is "anytime an Investigator draws from one of the decks." Obviously, trading is not considered "gaining" but should an Investigator draw a Spell for purchase or obtain one via myriad encounters, yes your colleague would also draw a Spell .

P.S. …and if the colleague is Dexter, remember to draw two and select one.