i recently posted this in another thread, maybe it will help you:
for what it's worth, i can tell you that i have 0 battery problems now that my phone is rooted and i was absolutely furious when i first got the phone. same physical battery, night and day difference.
while the battery is fairly mediocre the real problem is that out of the box the phone is great but the battery it's atrocious...
in lieu of rooting:
turn off radios you're not using - especially 4g and gps, both of which will suck up battery at an unbelievable rate.
If you are using gps, get a car charger.
i use wifi over 3g but only to my preferred networks, ie home and work.
don't just let it search endlessly for wifi networks that arent there or worse, bad connections.
turn down brightness
turn down screen timeout time
avoid fancy cpu-sucking animation screens, backgrounds, themes and screensavers.
avoid task killers
move apps to your sdcard if possible
turn OFF push. push is a great idea at first - but it's not necessary. unless you're some power day-trader, polling every 5-15 minutes is probably fine. do you really need to be reading your email while the person who sent it to you still has his finger on the send button?
push kills battery and is, in my opinion, a gimmick - at least with today's battery technology.
technically i use push, but i also use an app called Green Power Premium which turns everything off when not in use and then connects and syncs periodically. Some people will tell you that push is actually more efficient than polling ever few minutes and they're probably right - but i get hundreds of emails a day so that just isn't the case for me. ymmv but i think the point stands - you probably don't need your emails as fast as you might think you do.
check what accounts your phone is syncing. do you need a stock ticker on your phone? Do you need the weather? it is nice to have, but how often do you want it updated? do you need the news?
is your phone accessing other accounts - like social media? facebook, twitter etc all take power and you need to decide how often you want them doing this.
chances are you'll learn as you go - i will say many people were pretty PO'ed about the batteries
finally - since this is a used phone, your battery problem could be a simple battery calibration issue. there are a million things out on the web about "calibrating" your battery by some variation of charging and running it down but since you do not have superuser access the only way that i know of for sure to reset the battery stats is to do a factory restore. since you just got the phone you probably don't have much on there but you can back up what you do have (files on the SDCARD such as pictures, songs, videos etc don't need to be wiped) do a factory reset and that could fix some problems. couldn't hurt.
hope all of this helps, good luck!
something else that might be causing you problems is bad battery calibration. I assume your phone is not rooted? If that is the case then you can try the various charging calibration methods out there which can easily be found on google (charge all the way, discharge, recharge - that sort of thing) or you can just do a factory reset and start over. the latter being my recommendation.
however in my opinion your best option is to root the phone which will allow you to reset the battery settings either in recovery mode or using a great little free app called Battery Calibration which you can find here:
https://market.android.com/details?id=com.nema.batterycalibration&feature=sea rch_result#?t=W251bGwsMSwxLDEsImNvbS5uZW1hLmJhdHRl cnljYWxpYnJhdGlvbiJd
this worked wonders on my device and unexpectedly this was the best part of rooting my phone, an evo 4g which had atrocious battery life out of the box - even with all of the various battery saving methods you mentioned above and on every android sticky on the internet...
There is a great group of folks over in the EVO all things root forum that are really helpful and knowledgeable. No matter what you do to your phone chances are we can fix it. 
