Whew, I just finished my first full season with an opera company and I would have loved this thread last summer, when I was preparing for my new contract. Not that I don't love it now...it's solidifying everything I learned this year, and I have a lead on cheap lozenges for next year!
I came into this ASM contract with very very very little knowledge of reading music. I can follow it, but I'm certainly not proficient at finding where we are if I miss where we're picking up from. When I'm in production, I practice every day at home with my score and a recording; I practice the entrance cues I have and make sure I can call a potential cue on any measure at all. Sometimes I write notes to myself in my score ("listen for the bass" or "faster than you think!" or just circling a pattern in a measure that is easier to identify than anything else going on). I've also found that learning about the composer helps me pick up on musical themes, but that's a longer, on-going process.
7 months later, I'm finishing up my contract with a bit more confidence in what it takes to be a part of an opera, and a whole lot of respect for those who have successfully made the transition from theatre to opera.