I'm a total newbie, but is it possible to hook up a toggle switch as a power button to emit IR signals, on and off? If so, what would the code look like?
Yes what you ask is absolutely possible. I'd suggest the switch will probably not toggle the power, but be used to tell the Arduino to transmit when it's in a certain state.
The code will look different depending what you're intending to do, but since you're starting from the ground floor can I suggest a few tutorials to get you going. Firstly the video tutorial series by Jeremy Blum is well worth checking out. The first one is here and he introduces the use of switches in the second, so it's not far in.
After you've watched those (and by all means do keep watching them - they're all very informative imo), Adafruit has a bunch of really good background and practical info on iR controls starting here which includes an example of sending iR commands to a Nikon camera.
Depending on what iR commands you want to send, modifying that intervalometer example to only activate on a switch being in a particular state rather than at fixed intervals, and dropping your own command structure in to transmit sounds very much like your project.
Please send more information on what you have and want to control.
Do you have a (TV?) that you have the remote to control it? This will let you read the remote to know what to send from your Arduino.