If you want to initiate a new Conversation with a contact, click the New Message button at the bottom of your Conversation List. This will open a new Conversation window, where you can enter the phone number you want to text, type your message, and send.
If the contact is already in your Address Book, you can also begin typing their name or phone number to search for the correct contact.
Watch the tutorial video on Messaging Basics here.
Watch the tutorial video on the Conversation List here.