You need a half decent iron (weller, antex ..etc) a decent solder sponge (instead of getting robbed on ebay for a tiny iron single sponge grab yourself a cheap cellulose cleaning sponge from wilko/asda ..etc, for the same sort of price you'll have about 6 cut sponges

)
Cellulose sponges are obvious from their texture/appearance as shown below, if possible I'd grab uncoloured/natural however I've used blue & pink before and they have worked perfectly fine.
You also need some decent flux paste/liquid (I prefer paste as I find it easier to pin-point) especially if you plan on soldering surface mount/small electronics, something like the paste below is fine:
http://www.ebay.co.uk/itm/Electroni...Home_Garden_PowerTools_SM&hash=item20ebe54c05
Soldering is pretty simple if you follow the correct protocol!
When soldering two points together you must first tin each cable/point/component before ever even introducing them together.
First flux and then tin each point using your iron making sure the tip is cleaned each time and a new SOLDER BRIDGE is created on the iron tip using decent solder wire. Unless your iron tip and solder bridge is shiny silver and mirror like in appearance you should wipe down and re-clean the tip and re-apply the solder bridge. Also make sure that once you have created a clean solder bridge on the tip of your iron that you don't hang about, the longer you leave the solder heating up on the iron-tip the faster the solder starts to oxidise and the quality significantly drops.
Once you have both components tinned nicely (this again is obvious from appearance, shiny silver/mirror like is good, cloudy/dull grey is a sign of the solder oxidising/dry joint and is not good and must be re-done)
Finally flux again both components that require soldering and introduce them together, create new clean solder bridge on the iron tip and touch the solder bridge onto the tinned and fluxed components. Due to the previous tinning both components will flow with solder almost instantly, now simply remove solder iron and hold points perfectly still until solder sets (this can be tricky and can be helped by either using a solder helper crocodile clippy thing for larger soldering jobs or I just make sure my kynar wire is taped down into position before soldering on tiny circuits)
The soldering iron tip should NEVER be held onto components/boards/PCB's for longer than a second or two, it really should be one almost continuous movement, solder bridge in, touch and away!
Holding an iron on delicate boards or components for any prolonged amount of time runs the risk of lifting traces and damaging components!!
If it is taking longer than a second or two to solder two points together then your tinning/fluxing or solder-bridge is of poor quality and needs improving.
Always practise and simulate on old redundant circuit boards before attempting any delicate soldering on expensive equipment!!