Honesty, get the book. It's well worth it.
But in a nutshell...
1) First and foremost - assist the 1st AC. It's your job to take care of the people above you. Get them water, food, whatever they need. The 1st AC should never have to leave the camera, so you become their lifeline. And you should be ready at all times - NEVER SIT DOWN!
2) PAY ATTENTION DURING BLOCKING! Rehearsals are key for a good 2nd AC, because you need to be laying marks. Once marks are down, the 1st AC can then start grabbing preliminary focus marks.
3) Slating. This is so important and bad slates should never happen. Pay attention to what lens you are on - if you're on a wide lens, then you know you can bring the slate in closer. Also, keep your slates professional - I typically use military letters (it helps the editor and makes the script sup happy).
4) Lens and Filters. You need to make sure the lenses and filters are clean and free of dust - at all times. NEVER HAND A 1st AC a dirty lens - bad karma.
5) Camera Reports need to be readable and correct. There is no excuse for bad camera reports. If you need to, recopy the reports at the end of the day - the lab, production office, and DP will praise you for great reports.
6) Film Inventory - DO NOT SCREW THESE UP. If you are off in the slightest bit - you will get fired. So, double check your math and make sure everything is added up correctly.
7) Equipment Forms - You may also be in charge of the equipment forms. Make sure you have every piece of equipment at the end of the day and after every company move. You need to make sure everything is well taken care of. That also means - leave at least one latch secured at all times.
I'm only barely touching on all the responsibilities of 2nd AC. Like I said, buy the book. It's really an investment not an expense.