First contact?
In the early game: Plop huge piles of sats down on warp points as far out as possible towards your new rival. Colonize nearby planets if you haven't already so you can support ships to stand with the sats. It's all about the 'land rush' in the early game.
In the mid or late game it depends on your situation. If you've got lots of enemies already and your 'new' contact cannot easily send colonizers into your space make friends and get some trade going. It helps both of you get stronger compared to your current enemies. If they are close enough to crowd your territory you might have to stall for time until you can reduce your current enemies to manageable size. Unless you are already MEE, in which case you can just accept their declaration of war gracefully and queue them up for slaughter.
