Build Infrared Camera Remote
Using the Arduino shouldn't be any different than any other microcontroller.
The IRremote library is my go-to library for any IR related stuff.
Power shouldn't be an issue, look at the Moteino from LowPowerLab and check out his coin cell battery tests. It's definitely possible. Not with a full blown Uno, but with a bare chip, yes.
You want to burn the bootloader on the IC first, before you can start writing Arduino code. Check out this tutorial: From Arduino to a Microcontroller on a Breadboard. It's the same process for an ATTiny, you just have to look at the datasheet to see where to plug things into. Specifically, MOSI, MISO, SCK, and Reset pins. The Tiny AVR Programmer is also a good choice. It's meant for the 8 pin micros but it has an ISP header so you can use it for almost any chip.


This may be useful for more information about decoding IR signals:


EEVblog #505 - IR Learning Remote Control Hack
EEVblog #506 - IR Remote Control Arduino Protocol Tutorial