How to connect 10 coin vibration motors to UNO?
I would suggest a pair of ULN2003 chips.  These are 6 darlington transistors in a single chip.   Two chips will give you the ability to connect 12 motors.
Each one needs an IO pin to control it - if you want speed control then you will have to look into adding extra PWM channels. For just ON/OFF control any IO pin will do (even analog ones).
10 motors running at the same time will be up near the limit of the Arduino's 5V pin current supply, so you really should consider a separate external 5V power supply (maybe a USB phone charger) of 1A or more to power everything (connect the power supply to the motors and the 5V pin of the Arduino).