A trick one of my electronics instructors taught me many years ago is to put the wick on the solder joint to be removed, set the iron onto the top of the wick then pull up on the wick and wrap it around the tip of the iron. Heating the wick higher up from the joint causes the solder to flow up into the wick higher.
Once you do it a couple times it becomes second nature. Also, use flux.
Do you have a good soldering iron with a good tip set to the correct temperature? That's step number one. Then put the wick right over the joint, make sure you have flux or generally "wet" your soldering iron's tip (really using the "side of the tip" to heat up a wider amount of wick is an option).
I used to do this all the time but now I have a cheap crappy soldering iron and that makes it much harder. I hardly do any soldering these days so haven't bothered getting a good one.
The tricky bit is really melting the solder, getting it to flow, while it's in good contact with the wick.
Once you do it a couple times it becomes second nature. Also, use flux.