Some equipment you'll need is a motor controller of some kind. You can use a microcontroller and hook it to an H-Bridge if it is DC.
By remote I'm taking it as being wireless in some way. You will need a reciever for the remotes signals, which will be connected to the microcontroller. If it is not wireless, then hook it straight up to the microcontroller.
I do believe it is possible to make just an electronic circuit, but I am unsure of what types of remotes and such you are using. If the remote is wired, then you can take a look at something Knex puts out. Wireless is going to be a good deal more difficult.