This depends on the messaging app you're using (and likely the phone model). Most apps will have an attachment option (either a clip or a plus sign or something) next to the compose field. Additionally you can always go to the source of the image (camera, Gallery, etc.) and use the SHARE menu. From there, your messaging app should appear and let you select the conversation this needs to be sent into.
Some phones, like newer Samsung ones, allow you to drag/drop the image but this usually works only between Samsung apps (i.e. Samsung Gallery into Samsung Messages).