your car has no hitch reciever at all rigth now?
so you'll first need to get a 2" class III receiver assembly specific to your car, I believe Draw-Tite, Curt, and Reese all offer these for that generation Outback.
2nd, you'll need trailer hitch wiring with a 7-blade RV connector. this will require both a trailer light
converter module, which you connect to your existing tail light
circuits, this can be hidden behind a panel on one side of the back of the wagon, and is connected to various pins on the 7-blade, second you'll need to run a fused heavy gauge power wire (for the trailer charging circuit) from the battery
to a relay then onto to the 7-blade, the relay would be triggered by your ignition circuit, 3rd, a heavy gauge brake wire from under the dash to the 7-blade. the brake controller mounts under or on the dash as convenient, and needs that brake wire, a power wire (which can be wired to the same relay as is supplying the charge power, a ground wire, and also needs a wire to the brake pedal switch so the brake controller knows when your brakes
if your Subaru has an automatic transmission, you should ask your mechanic about installing a heavy duty transmission cooler, and possibly an aux engine oil cooler, too. If your Subaru has a CVT transmission, erase everything I said above, sell the Subaru, and buy something else which comes with a class III tow package to save most of the grief above.