How to fix my broken porch lamp?
Partial answer is if you don't have and don't want to purchase a reliable electric meter/voltage tester than you should hire an electrician, the meter is to ensure the circuit is truly dead off. Don't use a $20 cheapo multimeter on mains circuits they have poor fusing and are dangerous. Always begin by checking the meter is working by testing a live circuit.  

If the wiring just comes through a plain hole in the siding without an outlet box then it was not installed properly, it will need a remodel-box installed, assuming the remainder of the wiring install is acceptable this is a simple matter of buying the right size for your lamp's mounting screws. If there is no box and the wire looks old, less than 6 inches of extra, undersized, or lacks a ground wire then hire an electrician. 

If there is a box, is it the right size and style for the lamp base? It is somewhat odd to have it screwed right into the siding rather than the box, but not inherently wrong as a few are designed for that. If the screws pulled out due to wood rot then you have much bigger issues, if they were just undersized screws then you can put in some wall anchors of appropriate style and size.