I'm sorry to say you have a lot of work ahead of you. First, once the contact is selected by the user, then you need to extract the phone or email yourself. If there are multiple tel numbers or email addresses, you probably should then prompt the user which one to use - by using a UIActionSheet or a table. With a phone number, you can create a telephone URL and send that to the shared application, which causes a call to be made (there are lots of examples here on how to do that).
With an email address, you need to use MFMailComposeViewController to create an email, and then you add the one known address in for the user through the delegate. There is also a sister class, MFMessageComposeViewController, for sending SMS messages.
I did this exact same thing for my company and it took me about 3 days to code and test the whole thing (all 3 options).
EDIT: A person can have multiple phone numbers and email addresses. You have two choices here:
use the delegate method you already are using, return NO, but save the "property" and "identifier" that the user has tapped on. That will be a phone number, email address, etc (it could be a an address too so you need to probe deeper. You can find examples of how to get the exact property with those two values here or elsewhere.
you can use "peoplePickerNavigationController:shouldContinueAfterSelectingPerson:" to not show the user the person's attributes, but simply to indicate this is the person they are interested in contacting. With that persons record, you can find out how many email addresses they have, and if its only one then your work is done. If not you have to ask the person to tell you which one. [This is how I did it]