How can I control a motor via the internet?

If you have a computer at the other end to receive the internet then it's a bit easier, you can pick up microcontrollers which can interface with the serial connection on the computer really easily (large percentage have serial comms peripherals or you could just bit-bang a virtual serial port on the MCU) and then you could simply send the appropriate control data down the serial connection from pc to mcu and then send the appropriate motor control signals from the mcu to motor.

You could get usb compatible mcu's and the likes, but they are often sold as surface mount devices and thus rather more difficult to attach to boards with their annoyingly small pin-pitch and they are more expensive than a serial-enabled mcu and probably a good bit harder to program for as you need to waffle about with the usb HID spec, which I can't say I know much about so maybe you won't have that hurdle.

I'd recommend you stick with a serial port connection, it's simpler and if it's just a hobby/school project, it should be absolutely fine to use that.

you're able to try a % (programmable logic controller) they don't look to be too unfavorable costly and that i've got self assurance they do cause them to IP controllable. you would be waiting to apply the %as a team of switches to regulate all your lighting fixtures.