Clock input of a D Flip Flop
You could use a tactile pushbutton. They're very cheap and useful if you want to "step" through a design, but you'll need to make sure to debounce them to see accurate behavior.

You could also use a TTL oscillator or crystal. These are simple packages that will create a clean signal, but they will be at a fixed frequency and most likely the smallest one you can get easily will be in the kHz range so this may be too fast to observe individual edge behavior.

You could create a 555 timer circuit using a potentiometer to vary the period of the output, and you could configure it to be monostable multivibrator if you want a single clock cycle. This is cheap, easy, and the parts are easily available.

I don't know what kinds of parts you have on hand but personally, the solution I'd use is connecting a small microcontroller like an Arduino of Teensy to it. This has the advantage of allowing you to quickly create custom behavior, like every time you press a button connected to one of its inputs it creates a pulse of a given width. Or, if you want to go from a 1Hz output to a 1kHz output, it's as simple as changing a variable in code rather than having to calculate (and possibly purchase) new resistor values. You could also use digital inputs on it to measure points in your circuit and store their state. 

Without knowing much more about your application, it's hard to say which is the most fitting.