for quickness sake, i actually bought the 20/40 RS iron.. it's a little clunky and nowhere near as nice as the weller it's trying to pretend to be but i can do smd 0603 with it, and sot-23 chips (although admittedly the six-pin variant was a PITA).
I want to mention.. what a great crowd, wonderful advice from every angle.
a couple things to add my two cents..
1) get a loupe.. you can get a cheap 8x plastic loupe for under $10, and you can get 8x or 10x magnification it's infinitely easier to double-check your joints.
2) somebody mentioned a 'bad joint doesn't look right'.. more specifically.. typically either a 'cold' joint or a 'fractured' joint..
2a. a 'cold' joint happens if one of the parts you are joining wasn't hot enough.. the solder will 'wick' very well onto the 'hot' part but 'repel' from the 'cold' typically.. if you are soldering onto a lead coming through a pc board, the shape rather than being flat, smoothing out to the board, the bottom of the solder will either be vertical or even curve back in (it will be round or spherical vs conical).
2b. a 'fractured' joint happens if you move the part while the solder solidifies.. the joint should be shiny like a mirror.. if you move the part exactly when the solder solidifies, it will in-effect be like frosted ice.. just as water when it freezes slowly w/o motion ends up being clear as glass.. but if it's in motion when it freezes is opaque.. solder does the same thing, so easy way to tell if the joint is good is that it's smooth and shiny.
3. 63/37 solder.. find some.. get some.. 20ga.. much easier to use for smaller stuff.. i typically just cut off a foot or so at a time and make a little spool to hold in my fingers like 1 1/2 inch diameter.. the difference between 60/40 and 63/37 solder goes right back to 2b above.. the exact mix of tin/lead makes for an exact transition from solid to liquid state.. there is no 'slushy' temperature where the tendency to fracture is high. I found a POUND roll for like $15 at an electronics store about 15 yrs ago.. i'm about 20% done.. for me.. a lifetime supply.
4. hitting a point home others have mentioned.. clean shiny stuff.. sanding before soldering.. and pre-cleaning the soldering tip and pre-tinning the soldering tip... i would never solder w/o a sponge handy.. and i always tin the tip before and after use.. good to tin the tip just before turning it off.. so it keeps the tip from oxidizing until the next use.. you'll just heat the blob of solder on the tip next time you use it and wipe it off on the sponge before you use it.. it keeps the tip clean.. the rosin in the solder acts as a cleaning agent and keeps the tip nice and shiny.
5. 'heat bridge'.. you'll notice that the tip of the iron won't transfer heat to a part very well unless there is some solder between the tip and the part.. a typical procedure is to pre-tin the tip... and position the tip such that the little bit of solder on the tip bridges the space between the iron tip and the part... best.. if you can touch both parts (say.. pcb trace, and resistor lead poking through).. so they heat evenly. I always try to heat the part and apply the solder from a different angle... a good way to prevent cold joints, and you'll see the solder flow really quickly and evenly when the parts are hot.. .caveat.. it's possible to damage parts with too much heat.. so quickly heating soldering and removing heat is good.. heat sinks to keep parts cooler is a good thing to have.
I think that's it for 'lessons'.. i have to mention that i just got the 'cold heat' soldering iron as a gift, and.. i've been soldering for about 27 yrs (i'm 36).. and it's quite a little thing.. it is not going to replace any mainstay soldering tools, there are better ways to solder most things... however.. for certain applications it's perfect. Say you want to solder a wire to a switch or solder lug on a speaker, larger items like this.. it's awesome... took a while to figure out how to use it exactly...the commercials are misleading, making it look like it works as fast as spot-welding (which is basically what it is)... it uses the concept of 'spot welding' to use the item you are soldering to generate the heat.. the tip is actually a semiconductor (made of mostly carbon it would seem)... split in two, so power goes down on half, through the conductive item you want to heat, and back up the other half).. The 'trick' is that it takes a while.. soldering on to some fairly small terminals it took 12-13 seconds to heat it up nice n not to make a clean solder joint, but it worked perfectly, with no pre-heating like a normal iron, no plug like a soldering gun.. and when it's done, just like they show in the commercials.. it's instantly cool enough to touch with your finger.. technically.. it's probably 300-400 deg.. (it was just in liquid solder).. but is made of carbon with virtually zero specific heat so your cool finger cools it down so quickly you don't feel it. (just like how you burn your hand if you touch a pot in the oven, or the grates.. but not if you touch the same temperature aluminum foil).. In any event... for those types of jobs, not having to plug, not having a big bulky gun, not having the dangers of the heat of the iron.. it's genius.
Good luck learning to solder.. be careful... don't breath the smoke (i habitually blow just a little when soldering to keep the smoke out of my eyes).. be VERY careful if you blow to cool... i got too close once and burnt my lip.. i'll never forget that!
-awr