There are a variety of ways that a delay of game could be called on the defense.
The rarest of those is through having illegal equipment. Each time a ref discovers illegal equipment prior to a play, the offending team is charged with a timeout. If they have no timeouts, then they get a delay of game penalty.
A more common way (although still pretty rare) is for the defense to not "promptly" get their substitutions on the field and their replaced players off the field. The offense is prevented from running to the line of scrimmage and snapping the ball if the defense is still in the process of substituting, so the defense has to get their substitutions completed in a reasonable period of time. I would imagine this is a judgment call by the ref that is only made in extreme instances.
Also, if you've got coaches or players who are not in the game that are on the field of play during a play, or are between the sideline and coaching line during a play, then a delay of game penalty will be called.
If you call a timeout but then, at the end of the timeout, your team is not ready to play, then a delay of game will be called.
These are all relatively rare. The most common delay of game penalty you'll see on the defense (or, at least, the most common ones that I've seen) is when defensive players are deliberately being slow to unpile after a play, or are otherwise holding down/back offensive players and preventing them from getting back to the line of scrimmage for the next play.