So how do I control all of the stuff on this beast with a radio?

Well there are several ways to do this lets start with the most simple. Your Radio kit comes with handy little critters called servos. These guys are cool. They are basically little motors that can be commanded to turn to an exact position by the transmitter. They are powered and controlled by the receiver in your robot. They come in many sizes and their torque is rated in oz/in. We have used some MEGA servos in S.L.A.M that have 14 lbs of pull to apply the steering brakes. So by using a little imagination and creativity and some linkages. You can use them to trigger electrical switches, operate control valves for air or hydraulics , or even operate the throttle on a gasoline engine. I told you they were handy little guys.

Simple control of electrical devices
On both of our robots S.L.A.M and K.I.S.S I use servos to control all of the electrical devices except for the main drive motor on S.L.A.M which uses a Vantec speed controller. Basically I use the servos to trip little micro switches that control things.  Like the gas engine starter motor, the engine kill switch or even the relays that control a linear actuator that I use to shift the transmission on the robot K.I.S.S (See the picture below)..

Basically as the servo arm rotates it hits the switch trip blade and causes the switch to actuate. Usually I connect ground to the common terminal of the switch and then I connect whatever I want to control to the normally open terminal of the switch. So all you have do to is provide the plus voltage to the other side of the relay or solenoids control coil to complete the circuit. Up to several hundred amps can be controlled with the right  size solenoid.
See I told you this is a very simple way to control electrical devices.
It isn't considered very elegant but it works well and the switches can be found at most electronic stores. (A note about solenoids they come rated as continuous and momentary) If what you want to power has to stay on for more than a few seconds always use the continuous type.

They above system can also be used to control a linear actuator by creating an electromechanical H-Bridge using a couple of relays. The schematic below shows how the relays control the direction of rotation of the motor. It also has two limiting switches to control the minimum and maximum travel of the actuators arm.
In this drawing the servo controls switch 1 and switch 2
When the servo triggers switch 1  and sends 12vdc  through the limiting switch (switch 3) that energizes the relay (K1) which makes the connections to the actuator motor running it forward until it reaches its desired position. Then a lever that would be attached to its arm trips the forward limiting switch switch 3 and the motor stops.
To get the actuator to return home the servo triggers switch 2  and sends 12vdc through the limiting switch (switch 4)  and it energizes the relay (K2) which reverses the polarity to the actuator motor and runs it in reverse until a lever connected to its arm trips the reverse limiting switch
(switch 4) and the motor stops in it's home position.

 So now you have seen that controlling electrical stuff is pretty simple with servos.

The other way is to do it all electronically you can buy solid state boards that can read the signals that come from your receiver. There is  an H-bridge controller like the one mentioned above.  Also there are R/C solid state switch boards. And some other hard to get stuff and it's all available from  Team Delta

Of course mechanical controls are even simpler. Because all you have to do is connect a linkage from the right size (torque) servo to whatever you need to actuate.  One of the things I like to use to make linkage is piano wire .053" is my favorite size. You can buy some at your local music store. If they do piano repair. It is very strong stuff.