Hey all; it's me again. I've been working on my very first integrated circuit (is that even the right term?), and I've somehow absorbed enough understanding to assemble a circuit with a LilyPad Arduino to blink seven LEDs when I want. All of my components are arranged and working with one another, and instead of using conductive thread, I've used insulated wire to make the connections. Now that the circuit works, I'd like to reinforce the connections with solder. In particular, I need to reinforce the contact points on the lilypad's pins. I have a 15-watt soldering iron that(it claims) only gets up to 590 degrees F. If I use it to solder the connections on my pins, will it damage the lilypad? I'd really rather not try it until I get another opinion...
I've never soldered a lilypad, but from what I've seen, I see no reason why you couldn't. If you are really concerned about it, just keep the contact time on the pads as short as possible (enough to flow the solder well); use of extra flux (beyond that in the solder - get some liquid or paste flux meant for electronics - DO NOT USE flux meant for plumbing!) might help here.
A work colleague of mine advised that I not employ what he called a "cold solder." He explained that a cold solder is where you drip a little bit of melted solder onto your contact point so as to avoid overheating your components. I don't suppose he was right, was he? It sounds like that would be an ideal way to handle this sort of situation, but from what I gathered, such a method is very messy, imprecise, and makes less stable joints. He suggested that I instead heat the contact point with my iron (after applying flux) and then touch the solder to the contact point, which would melt it and "soak" it in between the wire and the pin. Since I want to avoid overheating the pins, maybe I'd be better off compromising and pressing the solid solder to the pin, and the iron to the solder just long enough to melt it in place. Would that work?
He also suggested that I could use alligator clamps to create heat sinks on either side of the solder to protect the components. That would be a good idea for all my other contact points, but it won't help the ones on the pins. Still, I think I'll keep it in mind. 
It helps to work with people who used to do this stuff for a living, but it also helps to have the internet at your disposal too.
Shuko:
A work colleague of mine advised that I not employ what he called a "cold solder." He explained that a cold solder is where you drip a little bit of melted solder onto your contact point so as to avoid overheating your components. I don't suppose he was right, was he?
Do people purposefully do this? That's called making a "cold solder joint"; the solder is hot, but it comes into contact with the cold joint surfaces (the wire and the pad), doesn't wet the surface properly, and "floats"/"beads up" or doesn't fully adhere. The joint is then very weak, and likely has high resistance.
You do not -ever- want to make cold solder joints - they cause all kinds of bad juju in circuits.
Shuko:
It sounds like that would be an ideal way to handle this sort of situation, but from what I gathred, such a method is very messy, imprecise, and makes less stable joints.
Yes.
Shuko:
He suggested that I instead heat the contact point with my iron (after applying flux) and then touch the solder to the contact point, which would melt it and "soak" it in between the wire and the pin.
This is called "soldering" - it's how you are -supposed- to solder (more or less). The trick is applying the right amount of heat for the right amount of time; with a properly sized and fully up-to-temperature iron, and proper flux and solder (and properly tinned), it shouldn't take any longer than a second to make a secure solder joint. The heat transfer to other components via traces and such will be minimal. If you're holding the iron on the joint for longer than a second, you'll likely damage the pad/trace long before the component.
Shuko:
Since I want to avoid overheating the pins, maybe I'd be better off compromising and pressing the solid solder to the pin, and the iron to the solder just long enough to melt it in place. Would that work?
Not likely, or it wouldn't work well. Just make sure your iron tip is well tinned, add some extra flux to the joint, and apply the solder and tip to the joint, flow a bit of solder in, then remove the solder and iron tip. It should be one smooth motion (it takes practice), and it shouldn't last longer than a second. If you think the joint needs more solder/work - move on to the next joint to allow it to cool, then come back to it. Something else to keep in mind is to note where the traces from the pads lead to on the board (where and when you can), and solder to pads opposite or away from the same areas being led to. For instance, if a row or set of pads all lead to the same side of a chip or other component, but others elsewhere go to the "opposite" side, alternate sides to keep heat concentration down. You might also gently blow on the joint - after it has fully set up (any disturbance prior to this can lead to a cold joint) - to cool it down.
Something I typically do for larger component leads when I solder is make sure I have a small blob (not dripping or anything - very, very tiny) of solder on the end of my iron (this is easier with a wedge tip iron, vs a pointed iron tip), and I apply that to the pad; the heat transfers quicker from the iron to the pad, and I can quickly add the solder in.
Shuko:
He also suggested that I could use alligator clamps to create heat sinks on either side of the solder to protect the components. That would be a good idea for all my other contact points, but it won't help the ones on the pins. Still, I think I'll keep it in mind.
This can be done if you have long leads and such, but there isn't really a way to do this on the Lilypad to protect, say, the ATMega processor, because of the SMT package (in the case of a regular Arduino, you would just solder a DIP socket in place, then plug the chip in later). If you were soldering thru-hole components (transistors and diodes, mainly), you could clip an alligator clip on to the component to soak up the excess heat (ideally, you use a special heat-sink clip instead of an alligator clip - also, if you do use an alligator clip, you should use one made out of copper, and perhaps file the teeth off to give more contact surface).
I think you are overthinking this whole thing though, actually. Consider how the Lilypad is put together: Solder paste is silkscreened in a process onto the component pads, a pick-n-place robot places the components onto the pads, then the whole thing goes into a reflow oven that heats the entire board up to a high enough temperature to flow the solder. The components can take the temperature fluctuation; they're designed to (because they have to go through this reflow process). Thru-hole designs go through a "wave solder" process, where the "bottom side" of the PCB is passed over a trough of molted solder, and a wave is induced into the hot pool of solder whose crest contacts and "flows" solder onto all of the connections. Once again, high temperatures, but short time periods save the day (really, wave soldering - from a temperature standpoint - is more gentle than oven reflowing - commercial PCBs sometimes have to go thru both processes).
You'd probably be ok with just some regular solder, maybe some extra flux, a good, clean, tinned, and up-to-temperature soldering iron, and some practice - to make solder joints for these connections quickly and accurately.
If you suspect you might have problems, practice your soldering for an hour or two on an old PCB of some sort, and some wire or junk parts. With practice, you'll get the hang of it, and you'll be able to then confidentally tackle your Lilypad.
Good luck.
Thank you so much for your help! I suppose I was underestimating the hardiness of my microcontroller after all. Still, I'm going to do what you recommended and practice soldering before I actually work on the real thing. I have zilch experience in it, and I need to get some before I'll feel comfortable.
Just one question for you: what is "tinning" the soldering iron?
Tinning is coating with fresh solder. Wipe the bit clean on wet sponge, apply new solder.
Shuko:
what is "tinning" the soldering iron?
This is the process of melting a tiny bit of solder on the tip of the iron. The reasons for this are that the flux in the solder will clean up / de-oxidize the iron tip (oxides cause an insulating barrier) and also the fresh layer of solder creates a path that will more readily flow heat from the iron tip into the joint that is being soldered.
Proper tinning involves wiping the tip on a proper cleaning surface, usually a wet sponge, and then quickly adding a tiny bit of solder to the tip. If done correctly the solder will immediately flow across the iron tip and make it nice and shiny.
Also note that it is important to tin the iron again when you're done making a solder connection and you will be setting down the iron for a while. The hot iron sitting in contact with the air will cause oxides to form on the tip. Tinning the iron will cause the oxides to be formed on the fresh solder layer as opposed to having the tip itself oxidize and thus be slowly destroyed. As the tinned iron sits there you can see the solder on the tip lose its shine and eventually get dark and dingy. This is why it is important to wipe and re-tin the tip when you're ready to start soldering again.