Most Phone battery's nowadays are li-ion, these are designed to be constantly topped up charged, you shouldn't let them get too low, constantly, they don't have a lot of zero to full charges capability.
By design li-ion batteries usually charge fast charge to 80% then trickle charge to 100% the first 80% can take two hours and the next 20% can take 2 hours, so around four hours in total. This is usually fine for most charging and overnight is fine too, if you leave it charging for up to 500 hours it wont damage the battery.
Sometimes the first time the battery is charge the calibration is off...
in this case use the phone until the battery dies, then keep trying to turn the phone on and get the last battery used for the next 10-15mins.
When totally dead plug in and leave phone charging, but make sure the device is off.
Then when fully charged (id say leave over night) remove and use as normal, but dont let battery get below 20%, and this time plug it in and charge with phone on, battery should then be working ok!!
If not... either an App is draining the battery, go into settings, about and battery usage and see whats been eating the battery, mine used a lot of maps and wifi sharing when i first got it but last two days on moderate use now!!
give it a try and if still crap take it back!!