I have 4 motors connected to their own ESC (that is connected to a power distribution board), how do I connect this to Arduino uno? (Drone)
Here are just some clarifications for you:


Signal pins don't have to be connected to PWM pins. AFAIK, any digital pins should work.
All grounds togheter! Glad you got that right!
Connect VCC of ESCs directly to the power supply.
Connect power supply to VIn of Arduino (not 5V because you are going to grill it!)




Uptdate


Yes, you can probably solder all the VCC wire of the ESCs togheter.
By power supply, I meant connecting it directly to the battery.





To power the Uno, connect the battery+ to the VIn pin of the UNO.