If that old ceiling exhaust fan in your bathroom is making strange noises or just plain not working anymore, don't bother trying to fix it. A new ceiling fan is affordable, easy to install and generally better than the old one that's there. The first thing you have to do for your project is to take the old fan out. The process of doing that is useful in itself, because it gives you a primer on how you'll be putting the new one in.
Cut off power to the fan at the fuse box.
Lay a tarp or towel on the floor beneath the fan. Remove the vent plate that covers the hole for the exhaust fan. You will either have to remove screws or pull down on the vent and unhook spring-loaded wire clips behind it.
Move to the attic above the bathroom. You will find the exhaust fan unit on the attic floor, attached to a joist with screws through metal support brackets and connected with electrical wires and an exhaust hose. Disconnect the wires by unscrewing the wire caps. Re-cap the bare wire ends from the house circuit and loop the wires up over a rafter or other high spot where they're easily visible.
Disconnect the exhaust hose from the fan unit by unscrewing the slotted screw that controls the metal band that holds the hose in place. Detach the other end of the hose from the exterior wall where it's mounted by unscrewing the screws that hold it there.
With your screw gun, take out the screws that hold the fan unit to the joist and remove the fan unit. Lay your piece of scrap plywood over the hole in the bathroom ceiling to close it until you can install your new fixture.