All "Person" card categories automatically have contact fields on their cards. 

Press the phone icon to add a phone number, the @ sign to add an email and the location icon to add an address. 

Don't have contact fields on your Card?  

You can choose which Card Categories you'd like contact details to appear on 

Go to settings and go to card categories and then select the category. 

Go to "Linked Fields", select Contact Details and save your changes.