How to set MINIMUM number of required fields?
You can use the Field validation module, and set up a validation rule using "number of selections".
The Field validation module has many validation rules you can set for any of your fields. It works by defining a set of validation rules at first, then you can assign that set to a field.

To answer your question, the validation rule you need to use is the "number of selections". You can define a minimum and a maximum number of values required. Just leave blank the "Maximum number of selections" parameter and set "Minimum number of selections" to your needs.