Damn, this is gonna be my first honestly useful post in the new board...
First of all, don't mind the characteristics bonuses too much for now. The ones you really need to care about are Strength and Toughness as they'll be the ones you'll apply to 1) boost your -melee damage-, 2) mitigate the damage inflicted upon you. Whenever you need to use the characteristic bonuses, the rules will prompt you. As you guessed correctly, that's the tens digit in your -characteristics-. Also, having an unnatural characteristics trait doubles that bonus. All marines start with Unnatural Strength and Unnatural Toughness. So say you have 40 strength. Your strength bonus will be 4x2= 8.
Whenever you take a -skill test-, you roll against your -characteristic score-, not the bonus. Basic skills can be rolled against without having trained in the skill, at a characteristic/2 penalty. So say you want to roll dodge, but you haven't bought the dodge skill. You have 50 agility, but to actually dodge you need to roll a 1d100 under 25. Serves you right for being a ballerina!
Oh, and download the errata from the FFG web site. Believe me, you'll want it as a GM for the sake of balance.