You should be able to turn this off in the Wordpress admin area - Settings/discussion/uncheck "allow people to post comments".
This only works for new posts. For existing posts you'd need to edit each one by clicking on "screen options" at the top right and putting a check beside "discussion". This turns on the box below the post that allows you to turn comments on/off for an individual post.
Or - you could do as JuggleDad suggested
(Side note - why did WP hide everything useful under that "screen options" button at the top right. Annoying!)