Ok, this should be easy:
1.) fill the keg with wine.
1b.) Cool Keg and wine down to about 32F
2.) Attach CO2 hose to keg, or carbonation stone.
2a.) Carbonation stones carbonate MUCH faster
2b.) If using carbonation stone, 2 hours carbonation, if using pressure equalization 1 week to carbonation.
3.) Carbonate to desired amount (20 - 40 PSI)
4.) Chill containers for the wine (reduces foaming)
5.) fill wine bottles and cap and wire shut
6.) Enjoy!
Personally, I think that counter pressure fillers are hard to use, but I do like the "beer gun". Easiest for me, is to chill the bottles and just fill with a spout.
I have a carbonation cap for my corny kegs, that has a CO2 nipple and under the cap is a length of tubing attached to .5 micron carbonation stone. This carbonates my beer/cider/wine quite fast as long as it is chilled well. I start at 5psi and increase 2psi every 3 minutes until I reach my desired PSI level.
Here is a carbonation chart to help you with your PSI goals:
http://www.northernbrewer.com/instructions/co2.htm
When starting to carbonate with the stone, I always purge the airspace on the keg twice at the low level. This means, turn on the CO2, adjust the regulator, wait for the keg to reach equilibrium, then open the safety valve at the top of the keg, this will force the oxygen out as CO2 is heavier. I do this twice before starting my main carbonation run.
Equilibrium carbonation means waiting until the liquid absorbs the CO2 over the course of about 1 week. Both methods work equally well, but the stone is so much quicker!