There are a couple few decent videos on youtube that can give you a start of an idea of what you would deal with doing a recone. It is quite simple, but can be tedious depending on the subwoofer. You basically cut around the woofers surround close to the inter basket to start. Fold or move around the cone to get to the spiders and start to cut around it as far out as you can until spiders are cut free. Solder/cut the leads from the terminals. Then lift out the soft parts (cone/surround/spiders/coil/etc) being careful to not get any debris in the motor. Once you have the soft parts removed the tedious part can come into play depending on woofer and such.. First you want to keep debris from getting into motor so put some tape around the motors gap. Now you will have to get all the remanding materials/glue from the basket leftover from where the spiders and surround were attached. People use whatever is most comfortable to them or whatever they have access to use for this. I tend to use a dremel for sanding of the remains and a wire brush attachment (IDK if it's called that, but its an attachment that is very effective to get the remains off quickly) at the beginning to get most of the stuff off. Once you have it all cleaned up, and you want it like the stuff wasn't there to begin with. Clean up the basket real well, take tape off motor gap, and make sure debris didn't sneak in the gap. Now, you have a good idea of how stuff works after doing that and the recone part is pretty easy. Just put some shims in between coil and motor of the new recone as your lowering it in place. Use CA glue for the spiders and you can use either CA or Goop for the surround and dustcap. Use clamps to press down on everything and I usually just set something about 5lbs worth centered on the dustcap after spiders and surround have dried. Dustcap is last.
This is a general idea but you need to check it out visually as well before you do it, so check them youtube videos, do more research then give her a go. I hope this makes sense and hope I did alright explaining, I had recently woke up from a nap and am still pretty tired haha.
Also, I do have a 18" SSA Xcon that needs a recone for sale if interested. It has everything still there for the whole procedure to be done too as far as removal of existing soft parts.