The process of recorking is pulling out the old corks and placing in a new one. This should be done every 15 to 25 years in wines that you are aging for a long time. The reason is that the wine acids and alcohol slowly soften the cork and then the wine leaks out.
The advantage is that if a little has, you now have the opportunity to taste that bottle and to top it up again. If the bottle is bad then dump it. I find many times that the cork is a mess and the hardest part of this process is getting the old one out. Many times you find that even if the wine level is in the shoulder the wine is good. That is a good wine to use for topping.
There are a number of lessons to be aware of in this process. The first is how to remove an old cork. Many times they are both very soggy and loose or they are dried out and want to break apart. I always start by trying to pull the cork with an Ah So https://www.youtube.com/watch?v=ila1A8VMRIY cork puller. It is two pronged, one to slip down either side of the cork so when you twist the cork out you are not ripping the center out of the cork. As you twist it both breaks the seal of the cork with the glass as well as keeps the entire cork intact. It works best on dried out corks but many times works on soggy corks as well.
The problem with soggy corks however is they are many times loose in the neck and when you go to try to push in the prong you end up pushing in the cork. That is when you require a screw type of cork puller. The best ones are the waiter cork screws. Look for one that has a long 2 inch screw that is Teflon coated and a double hitch lever so that when you are levering out the cork you are not stressing it sideways. I start by trying the Ah So and if the cork looks like it is starting to slip into the bottle I stop and resort to the waiter corkscrew. Use just a little tiny bit of pressure to start the screwing in process and then the screw should travel through the cork. Try to get it to go all the way through. The first try is to just lift straight up on the cork screw and if the cork is loose it should come out with ease. If that doesn’t work use the lever to start it and then pull straight up.
Wipe the top of the bottle with a wet cloth to remove any cap residue which may on older wines be lead.