A sprint is, by definition, a set period of time — usually two weeks. It starts on day one and ends on day x. Whatever is done between those two dates is the product of the Sprint. You don’t extend the sprint, you roll over work.
The primary trick to ensuring that stuff gets done is making sure that thegoals of the sprint are clear, and that the team agrees to achieve that goal during the iteration. If you have that part down, then getting them to make sure things are done is a matter of social pressure and making sure that the commitments are reasonable.
Scrum (which I presume you’re working under) is a team-based methodology, that relies on the internal pressures and commitments of the team and its members to achieve the goals provided. When I see “failures” of the team to deliver, it’s often because (1) the work is being dictated to the team, without their say, estimation, or approval; (2) there is no process of confirming consensus within the team as to the goal, and no way of holding people accountable for failures to engage; and (3) there is no form of retrospective to discuss why the goal was not met.