In Drive, select the document you'd like to collaborate on and click "Edit" from the toolbar. Once the document is open click on the File tab and click "Share/Permissions" from the toolbar. Enter the users name or email address into the "Invite people" box and click "Viewer" and select "Reviewer" from the dropdown menu to give them editing rights. You can type a message if you'd like and then click "Share". When the person you are collaborating with opens the document you'll see a box called Collaborators that lists the people that are currently editing the document. A cursor with the name of the person who is making the edits appears next to changes as they make them. Now you can both edit the document at the same time.
Tip: You can also share a link to the document. Select "Anyone with the link and invited people" from the "Who can access this file?" dropdown. Then click "Copy link" and you can share it via text, instant messaging, email, or any other way that you use to communicate.