Fully charge the battery with the phone on and when the phone is fully charged, unplug the charger and turn it off. When your phone is off, plug it into the charger and let it charge to 100% again.
This part is called a bump charge and can be bad for the battery. People have tried this in the past to get just a bit more capacity into the battery, because the charger will push a little juice into the battery before the battery's circuitry can say "stop, I'm full." Doing this once probably isn't going to do much harm, but it is a possibility. Doing it repeatedly can risk damaging the battery even more.
Not sure about the "bump charge" but i have seen positive outcome by allowing my device to turn its sell off when the battery is to low. When its off, plug it in and wait for it to fully charge. Then while the phone is still plugged in power it on. Let is sit for another 20 minutes or so charging then you can take it off the charger and use it. This has worked well for me and other people when trying to calibrate a battery.
I've also read on numerous occasions that once in a while the battery should be allowed to drop right down near zero. Microsoft for example suggest doing that with their Surface Pro tablets once a month. Lithium batteries aren't really happy about being near flat; but they aren't enthusiastic about being overcharged or overheated and that happens more frequently than a controlled discharge to near-zero.