Your approach is going to be different depending on how the windows are attached and the type of siding you have. The windows are typically attached by nailing through a 1" to 1-1/2" flange around the window directly into the window rough framing. The window flange is covered by siding and the trim, or just the trim.
To begin removal remove the exterior window trim and all glass in the aluminum frame. If you see the nailing flange, you are in luck and can simply use a pry bar to lift the nails out. If you have to get below the siding, use a circular saw set at the depth of the siding and cut around the flange to expose the flange and nails. You should be able to remove the complete window frame using a thin nail puller and hammer.
Depending on installation, it may be possible to use a reciprocating saw to cut the nails behind the flange without disrupting siding. Take a look and see what you get. Also, glaziers are really ingenious at getting windows to come apart. You might ask one in your area if he sees a way to remove the old windows with a minimum of disruption.