For some examples, check out the user submissions in the ArcGIS API for Javascript Code Gallery. Type 'zoom' in the search box.
To redraw the map zoomed to a feature, you can set the map extent (map.setExtent) to the appropriate geometry.
Two examples in the code gallery offer different ways to accomplish this, along with some other nice stuff:
I was wondering if anyone new if it was possible to zoom to a location within a certain distance. For example, I zoom to an address but want to zoom in a mile around the address and not to the point. Thanks
Jaclyn