How can I use arduino to control 4 motors speed and direction?
You have 2 questions here:


How to drive a servo motor?
How to drive a brushed DC motor?


Servos

Servos can be driven using a PWM signal. That's pulses between 1ms and 2ms at 50Hz, the length of the pulses controls the angle of the servo. There are 3 wires: GND, VCC, and one for the control signal.

Brushed DC motors

Brushed DC motors can be driven regulating the input voltage. This can be achieved by low-pass filtering the output of an open-loop op-amp driven by a PWM signal. This is a different PWM than for driving the servos, the high-level/low-level ratio determines the fraction of the input voltage you want to use to drive the motor.

A H-bridge might work but I am not familiar with this type of circuit.

I am not sure what kind of UAV you are making, sounds like a bi-copter. If this is the case you don't need to be able to control the direction of the rotation of the motors. You only need to hard-wire the motors to run in different directions, but the direction does not need to change in flight which greatly simplifies the problem.

This should give you enough leads to get going. If anything wasn't clear just shout :)