This article deals with replacing defective electrolytic capacitors, and relates to the article under Power Problems, entitled Keeps Clicking / Won't Power-Up.
Before you begin, you need to know that electrolytic capacitors have a polarity, and must be oriented on the circuit board correctly. Observe the markings and the plus and minus signs both on the capacitor to be removed and on the circuit board where the capacitor is mounted. These markings correspond to the two wires that protrude from the bottom of the capacitor that are soldered to the board. They identify the positive terminal and the negative. When inserting the new capacitor into the board you must orient it like the one that's in the board. If you install the capacitor backwards, it won't be long after you power up the television before the capacitor "pops" and is rendered useless. Then you’ll have to do the whole thing all over again.
If you go to your favorite search engine and search the phrase "soldering tutorial", you will find lots of information on how to solder.
It is good that you clean the tip of the soldering iron often (while it is hot). A wet spongue works well for this. Another thing is "tinning" the tip of your soldering iron. You must make sure that the tip of your iron is tinned, or wet with solder. This will cause the heat from the tip to transfer quickly to the place on the circuit board you are soldering. If your tip is not tinned, the heat won't transfer well and you may not be able to sufficiently melt the solder at that point, which would make for a poor solder joint (refered to as a "cold solder joint").