In truth, a 2P5T switch is what you might need. This would provide 4 alternate selections, plus bypass. Of course, if you plan to have a stompswitch to select between bypass and whatever circuit has been selected, then a 2P4T is sufficient.
Many, if not most, people would likely use a chicken-head knob to turn the switch. I mention this because if the knob itself has a pointing function, then you don't really need to use any sort of indicator LED to show which circuit is in play at the moment. Having said that, though, if you want an ultra-sexy unit that changes colour with overdrive type, then you will want a 3P4T rotary. One pole selects which LED and the other two poles move across the 4 different input and output connections. In truth, it is no different than wiring up a DPDT or 3PDT stompswitch, except that the input/output leads have more places they can go to.
If you wanted a real über-pedal, you could opt for a 3P5T (or 2P5T), with the 5th selection being an external loop so you could patch in whatever else you wanted, including something not yet built/bought.
So, how do you wire it? You will likely see tabs along the perimeter, and a smaller number of tabs on the inside. Ritate the swuitch fully counter-clockwise. Take your meter, set it to beeper/continuity-testing mode, and probe for continuity between one of the inside lugs and one of the outside lugs. Now rotate the switch one click to the right and see if the continuity exists between that same inside lug and the outside lug just to the right. If so, then you have a "map" of how the contact is provided.