Adding to @bstpierre's excellent answer, if you simply water and mow (at the right hight, you will find that the lawn comes back pretty quickly. Adding seed can help but grass can spread into bare patches pretty fast. In general, the best thing to do is to let the clover work. It can be an important part of a healthy lawn and it will save you a lot of headache if you leave it in.
Of course this depends on how big the patches of dead space are. If they are small (say, no larger than 6 ft across by the smallest dimension) I would just say water, possibly fertilize, and just mow. You may get some initial weeds but those will get quickly selected against by the mowing and the grass runners (annuals rarely if ever outcompete perennials if everything else is ok).
Dead spots are usually an indicator of a lack of water, and the live grass roots may go further there than you expect anyway.