Attach a contact to a text message

This is pretty straightforward:

Open Contacts

Find your Contact and open their Contact Card by tapping their name in the list

Scroll down to the Share Contact option

Contacts will first prompt for which contact details you want to share (name, addresses, email addresses, phone numbers, etc.)

Once set, click the check box. You'll then get the standard iOS share options where you choose how you want to share this data. Frequent/recent people you message with should be listed at the top, or choose the Messages icon to enter any other recipient's number.