This is supposed to be your project not ours. If you keep asking questions and expecting answers, you will never learn how to be an engineer. That is why you are training, isn't it?
I'm sorry to post such a negative comment and I don't mean any offence but you need to do your own research. You have been told how analogue joysticks work and you've been told about motor drivers. You need to work out the bit in the middle!
The internet is a wonderful resource of code and hardware examples: use this help to get a value from your joystick. Find a motor driver with the type of input you understand - it might be analogue, digital or PWM. Then find out how to convert your joystick value to the type of input required.
We all want you to become a good engineer and that requires hard work on your part - no shortcuts I'm afraid.
The left right movement of the joystick can be used to steer the wheelchair by differentially driving the wheels. The Y-axis of the joystick, or say the forward and back motion of the joystick can be used to vary speed and direction - pulling the joystick back from the centre-point could make the motors reverse direction. But in all this, do remember to keep a deadband around the centre-point of the joystick, wherein the values do not do anything. Otherwise you might land up with a wheelchair that keeps creeping even without any control input...
