I think the fic you’re looking for is The stars are behind him (and they are ready to fight) by arabellagaleotti! I’ve never read it, but it includes a scene of Tony and Bruce drinking tea and the quote you gave. Let me know if it’s the wrong one. 

As for how I find fics? Well, if I’ve read them then it’s usually pretty easy since I have a decent memory for details, but a lot of the time I can find fics even if I’ve never read them just by using the right search tools! Mostly I try to narrow down search results by any criteria given to me (characters, pairings, specific tropes, universe, etc). So for example, to find the fic you’re looking for I used the filters: 

Characters: Tony Stark, Bruce Banner 

Additional Tags: Alternate Universe 

Search within results: “space” (this looks at the summary, notes and tags of a fic - tagging is very unpredictable so this can be very useful) 

Sort by: Kudos descending (odds are the fic in question will be high on the list) 

I opened around 10 fics based off those criteria, clicked “entire work,” then used the find-on-page (ctrl-f on pc) feature to look for the scenes you remembered. In this case, I searched for “Bruce”, located the tea-drinking scene, then searched “alien” and found the quote you gave in the fic I linked above. 

A lot of requests are pretty easy - I’ll just plug in a couple of search criteria and it’ll be at the top of the list. Others are harder and need more time, and others I can’t find at all - whether it’s because of incorrectly-remembered details, vague memories that don’t give me anything to work with, or limited/improper tagging on the part of the author (or there’s the chance that the fic was deleted!).