is it possible? If so, how?
This is a noob question because its my first time using the pro mini
Yes you can.
One option is to just use 3x AA batteries in series and this is enough to power it.
Another option is to use a buck/boost converter (something like this) that can take a variable range of input voltages and boost or drop them down to 5V.
To run an arduino off batteries for any length of time needs careful considerations on design (remove LED's to save power, avoid the built in regulator, sleep the Arduino when not needed)
With the 3AAs, or a 5V source, connect to VCC and not RAW.
There is a 5v and a 3.3v version of the pro mini. If battery lifetime is an important issue, there is a variety of techniques to minimize power consumption, depending on your application.
A boost converter will squeeze that last bit of juice out of the battery, lots on eBay.
Or
.
Or grab a board designed to do this, and as a bonus you have built-in in RF, 4Mbit Flash and other perks:
Edit: extra features mentioned as bonus, you can use if you want.
musskopf:
Or grab a boarddesigned to do this, with built-in in RF and 4Mbit Flash:
Have you miss posted this as I can see no reference to RF from the OP or anyone else?
Have you miss posted this as I can see no reference to RF from the OP or anyone else?
Sure there's no reference to RF neither anything else... but you know, like driving a sports car to go to work. You get much more than you need, but I bet it's much more fun, specially at weekends 
Now seriously, complementing my previous post: Always take serious consideration before powering micros-controllers by battery without regulation as most kinds of battery will have significant voltage drop along its life, making your project work unexpectedly or simply mislead your power calculations by not using the whole energy on each cell.
For example, if you have 3xAA (or AAA or any kind of Alkaline 1.5V cell) you'll have approximately 4.75V at the beginning, but the voltage will drop down to under 3V by the batteries' end-of-life. Here from the Duracell Datasheet:
Now, if you have a sensor that only works from 5V-3.3V, you might start to get funny results... The problem is even bigger if you wish to use only 2 cells. Anyway, you can always monitor the battery voltage using an Analog port and behave accordingly. Additional info about kinds of battery and their characteristics here: Powering micro-controllers by Battery - Wisen.