I have found some pretty crazy things in No Man's Sky and I would like to share the finds with my friends outside of the game.
Is there a way to do this other than taking screenshots and sharing them through Steam?
No, there isn't. The most that is possible inside the game is the scan for nearby discoveries, and that usually only works when your friends are quite close by. Currently, Sean has said on his twitter here and here that multiplayer is included, but the servers are too overloaded to cope with it at the moment. This leads us to believe that it may be a while before "your friend showing up on the galactic map" is in the game. So that option isn't impossible, but highly unlikely at the time of writing.
Outside the game, Sean and Hello Games haven't made anything that links to the inside of the game, like an API, just yet. The community itself is working on some things, such as a list of all crowdsourced discoveries and more. However, apart from these and simple things such as recording and screenshots, there is no way to share your discoveries with friends.