The power requirements are often printed on a sticker on the back. If not, you'll have to measure the current like Phil said. Voltage is easy: if all batteries are connected in series just multiply the number of batteries by 1.5V.
Then you basically have four options: either connect the adapter leads straight to the battery terminals, drill a hole in the case and add a DC power plug, make a dummy battery pack, or take the adapter apart and mount it inside the battery compartment. I personally like the last option since you'll only have an AC lead coming out, without a wall wart taking up three sockets 😀
Keep in mind though, that the circuit might not be designed for AC adapter use. Batteries have a very steady voltage, slowly dropping over time. Voltage from an adapter may be more fluctuating or just downright noisy. Audio or video equipment can be especially sensitive to this.
Luckily, with a C-cell battery compartment, you'll have more than enough space to add extra capacitors if this turns out to be an issue 😀