NEVER run the phone until charging it the first time. That's batterycide.
Charge it until the phone tells you it's fully charged. Use it - without charging it - until the phone tells you to charge it. Go through 3 cycles like that. (It's called conditioning the battery.) If the battery is new it doesn't need to be conditioned, but you can't tell how long it's been sitting on the battery maker's shelf or the phone manufacturer's shelf before you got it, and conditioning doesn't hurt. Running a battery that's been sitting for a few months without conditioning it cuts its life short, so do it to every battery you get, and any time the battery's been sitting for a few months. (NEVER store a battery in the phone for months - always remove it to store it, and leave it at about a 40% charge.)
If you want to learn about lithium batteries, read the battery course starting at
BU-701: How to Prime Batteries – Battery University Cadex has no axe to grind, they don't make batteries, they make battery analysis equipment, so they've analyzed (and tortured and killed) enough batteries to know what they're talking about. (But you'll still get arguments from the experts about conditioning - some say that modern batteries don't need it. All I know is that my 10 year old V551 batteries, after a long storage and conditioning, still give me just about full life.)