The movie's director is probably one of the first things I look at. If I've enjoyed some of his other work then I will often look forward to watching it, regardless of positive or negative critical reception it may have met.
Assuming the director of the movie in question isn't a decisive factor, I usually check the score on IMDB/FilmAffinity and my soulmates' rating of the movie on FilmAffinity. Recommendations from people whom I trust in this department work just as well.
Leaving all of that aside, I'm generally interested in watching movies nominated for the Oscars aswell, mostly because I keep hearing/reading about them and curiosity usually ends up sparking.
I avoid reading reviews (even if they are spoilerless), and I don't watch trailers unless I come across one (in the cinema, on the internet, etc).