It may take a few days for the OS to fully profile the battery. Once you hit 5 days if you notice no change, you could have a problem that might require a factory reset or a visit to the store.
Your battery cannot be over charged. You can safely keep it in the charger until ready for use.
Your battery was delivered partially charged. Hopefully you charged it completely prior to use. If not, it may take a factory reset to get you back to full operation. To start with, fully discharge your phone, turn it off and then charge it fully. Do not fully discharge your battery very often as it damages the battery. Since your phone is fairly new and you probably haven't forgotten your gmail password yet, now is a good time to do a factory reset. Look in the FAQ section of this forum for hard reset instructions. It is best to not allow your apps to sync automatically during the reset (this is not because of the battery though).
If you have a standard battery, and you live in the USA, remove your SIM card. If you have a standard battery, you can reinsert it upside down so that it doesn't make contact and so that you don't eventually lose it. You can do this with the extended battery but no guarantees that it won't be damaged since it has to bend slightly to fit. Doing this is the same as setting your phone to CDMA only, except that the setting can revert in some instances.
In Settings -> Battery & Data Manager, the following settings can be used to help:
Battery Mode defaults to Nighttime saver but if you are around low signal during the daytime you may want to create a Custom Battery Saver to turn data off after 15 minutes during those times.
Data Saver defaults of off, turning it on if you have WIFI will default data heavy tasks to the faster and more efficient WIFI network. This is helpful primarily if you spend large amounts of time away from WIFI.
Data Delivery defaults are as listed below:
Background Data on. Turning it off will save battery but you will not get things that require background data (email, facebook....)
Data Roaming off. Unless you are on the road all the time this is the best setting.
Data Enabled. I think turning this off will default data to WIFI only. If so, that would be the same as Background Data off when you are not around WIFI.
Email and Corporate sync is greyed out, Look into Accounts to control this feature.
Social applications has two settings, Sync over WIFI only which should save some battery, and data delivery frequency which I believe is set to Push by default. Setting it to 60 minutes should save a bit of battery as well.
Under accounts, removing accounts can save battery at the cost of certain things. If you use the provided social networking applications then facebook sync will affect them as well as contact syncing. You can save some battery by ignoring those and downloading native applications for things like facebook. I'm not a twitter user and I suspect it could suck-down some battery juice, but I would bet a better app could be found in the market for it as well. Those built-in applications (bloatware) tend to gulp from the battery so I would avoid them.
The more kinds of accounts you sync, the more battery you use so if you can avoid syncing both gmail and corporate/yahoo/whatever accounts you'll save some battery also.
Turning off WIFI, Bluetooth and GPS during the day or more specifically when you are not using them will save some. If you are around a good WIFI signal though, you'll probably save more by keeping it on.
Widgets can use lots of battery as well, depending on the widget. If it uses data in the background like weather and news apps tend to, then it will be drinking from the battery. Reduce or eliminate as much as possible.
Same thing goes for apps. Some of them run continuously in the background and use data. Be careful what apps you load and do so slowly so that you can identify wasteful apps.
The Verizon apps have been known battery gulpers. Avoid them at all costs. You do know you already have a native navigation app for Android and don't need the Verizon one right? (that was a rhetorical question.)
If you haven't updated roaming, dial *22899. It may make you reactivate your phone (it did mine) but that is a painless operation.
If you didn't get an extended battery, it would be a good idea to do that, but don't try to swap between that and the standard battery, you'll confuse the battery statistics. You will have to let the phone adjust to the new battery though.
If you click on my name to the left you can look over my prior posts where I tested these suggestions and others to get an idea of what to expect. One other bit of advice is to use one of the battery saving apps in the market. Juice Defender is one I used on my Droid1 and liked, and I'm using it on my gTab as well so I can recommend it, but there are some who've said it has some problems with the Droid 3--and there are some who say it works well with it.
There are probably more recommendations out there but these are the ones that will do the most in my experience.
