Creating stepper motor driver using only TTL ICs
Here's how my approach would be:


Become familiar with the different ways of driving a stepper motor.  The Wikipedia article on stepper motors has a good summary.  The easiest way appears to be the Wave Drive method since only one phase is active at a time.

Write down the basic logic you'd need to drive the motor in one direction.  From the figure, it looks like it would be pretty simple to implement.  (E.g. if A was high, set B and clear A.  If B was high, set C and clear A...).  Now convert that to logic gates and flip-flops.
Verify your logic with a software simulator, or build it and capture the output with a logic analyzer or LEDs.  For the LED method I'd slow down the clock speed to a Hz or two, or even use a push-button for the clock signal.
Repeat steps 2 for reverse direction.
Combine the two directions on paper and see if you can simplify the circuit at all.  Otherwise you may end up with AND gates at the CLEAR pins of each flip-flop, which is fine.
Repeat step 3 with the whole circuit.


Step 5 kind of violates the 'make it work, make it right, make it fast' principle ('fast' being replaced by 'simple' in this case) so you can omit that if desired.