The latest version of Android only allows you to send images and videos as MMS messages, even though more is technically possible. Begin a new message thread, or enter an existing one in the Messaging app. Before typing any text, tap on the camera icon to the right of the edit box. This will allow you to select an existing photo or video, or to take a new photo.
If you select to attach a photo or video, you will be taken to the new Photos app. Note that while you can attach multiple images to a message, you can only attach one at a time and will need to repeat the selection process. You may also attach your location by tapping the map pointer icon (to the left of the camera icon). This will attach a Google Maps hyperlink and a screenshot of the location in Google Maps. If you have other types of file that you wish to share, consider uploading them to cloud storage services like Google Drive or Dropbox and creating a sharing link, which can then be sent via text message.