You can clearly see, comparing the underside with the top side that the pad for the fourth pin doesn't have a track. The remaining pads must be the two track ends and the wiper. I suggest measuring resistance with power off between pins of a similar volume control pot, while turning its shaft to figure out which one's the wiper and then which of the remaining two are the clockwise and counterclockwise ends of the track.
You'll need to make a bracket for the new pot to mount it to the PCB. I suggest cutting and bending tin plate (tinned steel sheet, cut from the bottom of a large biscuit tin or similar) to form it. Edges should be folded back and soldered to stiffen it , and tab legs left or thick wire legs soldered on to go through the mounting holes in the PCB. As there are only two holes for mounting tabs , you'll have to design the bracket to hook round the edge of the PCB, insulated from it with Kapton tape or similar stuck over the track that runs there, to get enough mechanical support. Prototype the bracket by cutting and folding thin card and trying for fit, then unfolding it as a template to mark the tin plate for cutting. Don't forget to add on any allowance for bent over edges, mounting tabs etc. that weren't part of the cardboard mockup!
Fit the pot, tags up, to the bracket with a nut, (You did check the clearance to the panel so the nut will be hard up against it when designing the bracket?), solder the bracket in place, and run wires from the tags to the PCB pads, taking care to get each track end and the wiper to the correct PCB pad even though that will probably mean the wires cross.
I think you've lost the pad from one of the mounting holes, so for that one you'll need to cut a very small rectangle of tin plate, trim the corners and make a slit in it to fit tightly over the leg protruding through the board. Push it over the leg and right down to the board so its in firm contact with the bracket also tight against the board, solder it, then at the end after you've cleaned up the flux residue from the PCB, and thoroughly dried the board, run a little superglue under it to firm up that leg. I'd do that leg first so you don't strain the remaining pad for the other leg.
These videos may help you start learning the craft of tinsmithing, i.e. the techniques required to work with tinplate successfully:
http://tinplategirl.com/category/videos/
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