Hi Paul-
I've been pretty much a hapless solderer most of my life. But today's world involves so many circuit boards, and I had several devices this year that were agravating me, so I finally determined I was going to find out how to fix the friggin things myself. 1 wireless PC mouse, 1 cantankarous microwave oven, and 1 TV digital to analog converter box that quit on us. All were finally repaired by my little self after watching a few of Ben Heck's shows online, and one online video of a repair of the same converter box as ours, that pointed out an inherent capacitor failure.
I modified some of the techniques to suit my situation, and will try to take some photos tomorrow for you - a picture is a thousand words they say, and God knows I am good at overwhelming folks with words. My big problem was my slight tremor that made holding solder or iron steady, and squeezing and releasing a solder removing suction bulb with any accuracy, impossible. Set aside some time and watch Ben's video, and perhaps pick a few others from his larder, and check into even more from other perpetrators re. soldering on YouTube. Some are good and some are stumbling and not so great, as is par for the course for the YouTube beast. But I got enough good stuff out of my time that I could effectively use what I learned to fix all 3 of my problem devices. Ben's were the most well produced and presented.
Ben Heck's shows have advertising, but the good thing about them being online is you can move the cursor ahead and skip over ads in the videos. Some of his stuff is hokey, but his fun attitude combined with real skill will keep your attention, and makes it easy to learn better techniques. One problem I had was I wasn't cleaning things properly when soldering. A wet sponge and a decent soldering station with adjustable alligator clips and magnifier really made things easier. As Ed notes, don't use an iron with too much wattage - 40W should be more than enough for circuit boards, but I wouldn't hold that much wattage on a joint too long; I used to use a dual-heat Weller gun, but it was way too much for circuit boards - probably did more harm than good. I like my 30W Dremel iron for these jobs, and use the very small diameter wire solder specifically designed for electronic circuits, not the big stuff you may have used elsewhere.
I opted not to buy the copper braid or the syringe-like vacuum device, as I modified my little portable vacuum cleaner with a tip that does such a super job of removing solder that I needed nothing else. That and the soldering station/vice helped minimize the issues caused by my shakiness. I will provide photos; but if you opt for braid or special desoldering hand vac, they are available at Radio Shack, Sears, and most hardware stores, Home Depot, or Lowes.
Here is one that demonstrates quite a bit of copper braid desoldering, once you get through the stumbling first part; I found no audio:
http://www.youtube.com/watch?v=BrAJpz9Mdm4and here is Ben Heck's basic soldering demonstration:
http://www.youtube.com/watch?v=FO9CHjdqBr8&list=PLwO8CTSLTkijrSW6DIFsQxcvjRo5fZ-y5-Joel