They will remove your current dish and supply a new one. All the wiring will remain, they will just connect your new receiver*. You only need a new receiver on the HD set, however, some prefer to get all HD receivers, even on SD sets, as it allows you to receive some channels that are only available in HD on every TV (the cost for new receivers is the only hinderence).
*Unless you're going from a standard SD receiver to an HD DVR in which case you'll need a second line run.
*Unless you're going from a standard SD receiver to an HD DVR in which case you'll need a second line run.