They'd need to know our culture if communication is an eventual goal. Assuming they have LLMs, this should be easy as we've been blasting a wide radius almost 100 lightyears.
Direct interaction would change us fundamentally and they know that, so they'd opt for a subtle approach. Probably politics with a mix of anthropology.
There's a nice short scifi novella by Chad Oliver called Blood's a Rover that explores this a little.