Done at a pace that will allow you to soak up The Hague's historical atmosphere, a minimal tour around the city center should take about three or four hours. If you stop to visit the main sights en route, you're looking at a very full day. At the very least, allow 30 minutes for each site you visit.
Before you start out, bear a couple of things in mind. First, as in all other Dutch cities, both walking surfaces and the weather can change at short notice; if you're going to be on your feet all day, make sure you're equipped with an umbrella and sturdy walking shoes. Second, most museums and galleries close at 5, and many sites are also closed Monday, so plan accordingly.