To see the international relationships, you need an Embassy with at least one of the Civs in question, and be at peace with that Civ.
Embassies become available with Writing, and setting one up requires a one-off gold-payment, either by you or by the AI (the latter happens more frequently at higher levels/ later stages of a game, when the AIs are less likely to be completely broke!).
You'll be prompted to set up Embassies immediately after you learn Writing, but never again. If you clicked "No" at this prompt (e.g. because you had no gold, or were at war with everyone you'd met so far), you can still set up Embassies later on via the "Espionage" screen -- which you can get to by clicking the little "E" button on the right side of the "currently active unit" box.