The easy way for someone who is not a hardware guy would be to connect:
A food dispenser that works electrically - I don't know where you'd find this.
An rs-232 controlled relay board, something like this: http://www.advantech.com/products/ADAM-4060/mod_1-2MLDI7.aspx
And an rs-232 over TCP/IP board, (AKA a serial port server) something like this: http://www.advantech.com/products/ADAM-4571L/mod_1-2MLDTN.aspx
That's assuming that by "remotely" you mean "over the internet".
You may very well be able to find the last two combined as one product, and I'm sure you can find cheaper ones.
The serial port server will come with a driver that gives you a virtual serial port. You can use either a terminal program or any programming language that can send data to a serial port to send whatever commands the relay board requires.