"[Connecting with your high schoolers] on non-academic topics [goes a long way] if you hit a rough spot later on.”
To connect (in this context) = to talk to and understand someone at a personal level; to communicate easily [with someone]. Usually with the meaning of "in a friendly way."
To go a long way [often with "towards something" (usually positive)] = to contribute [towards]; to be a great help [to];
to hit (informal, and in this context) - to encounter suddenly
A rough spot (idiom) - a difficult situation
later on - at a later time.