what is the best way to connect a motor to a pump so no vibration or at least small vibration??

 

With anything that has it's mass equally distributed around the axis of rotation

 

Use a flexible coupling. That's important for vibrations and alignment.

 

I agree with carlosramosr.
It is recommended to use flexible coupling to connect a motor to a pump.

If you want to learn more, here a link to an important flexible coupling manufacturer
http://www.ktr.com/en/products/couplings/productoverview.htm

 

Flexible coupling can absorb vibration if any.