How to connect laser module to cnc sheild v3.0

What is the best method TTL or PWM?

Not sure that you understand the difference between the two. TTL is a voltage specification for logic which is basically 0V and 5V for the two voltage levels. PWM, is pulse width modulation and consists of turning a signal on and off. The ratio of on to off determining an equivalent voltage. See http://www.thebox.myzen.co.uk/Tutorial/PWM.html

So this question

What is the Wiring digram off TTL and PWM?

Makes no sense.

How to supply power?

With a 12V power supply capable of at least half an Amp. Make sure the ground of the power supply is connected to the ground of the Arduino.