How can I add a window to my front door?
In a traditional panel door construction, the panels are held in grooves cut into the rails (horizontal pieces) and stiles (vertical side pieces). The rails and stiles are doweled and firmly glued together, and it is impossible to take them apart without ruining them. The panels are not glued in place, so they can expand and contract with the heat or humidity, without changing the overall dimensions of the door. 

If you want to try to replace one of the panels with a glass or perspex pane, you must carefully cut away the molding from one side of the panel. (You should cut on the outside of the door because windows are traditionally caulked on the outside.) Remove the wooden panel and use a chisel and sandpaper to clean up the opening. 

The steps, in cross-section: 



Then you can install your pane using standard glazing technique. 

You might also want to replace a damaged wooden panel with another wooden panel. In that case, instead of caulking you would install milled wooden strips, such as quarter-round or very small crown molding, to hold the new panel while allowing for expansion etc. 

One problem you will have is figuring out how much molding to cut away. You should carefully carve material away, about halfway along one edge, until you can see the edge of the panel, then extend the measurement to the corners. 

Alternately you may be able to break the panel and remove it without damaging the door. Cut out most of the panel with a jigsaw, notch the remaining frame almost to the molding in several places, and break out the remaining pieces. Once you have wrenched out the first piece, the others will come out quite easily. Then you can measure the depth of the groove directly and decide how much to cut away. 

I would call this an advanced-level project, because the results of your carpentry -- joinery, really -- and your glazing will be highly visible and in your face every time you enter or leave your house. 

If you have some artistic design or special effect in mind the results can be worth the effort. But if you only want to get some more light into the place, just buy a new door.