Get a digital multimeter.. less than $15 at radio shack.. get a telescoping magnet wand.

The sort of soldering you are doing there doesn't have to be too precise or pretty. You'll want to get more refined when you proceed to board work.

Also, in the soldering you show, you don't want to rely on solder to make a physical connection. (the solder shouldn't be providing the strength of the connection) Preferably, you'd clear out all the solder on that joint, and then wrap the wires around the lug (which likely has a hole in it). The physical connection is thus made by the wire itself and any stress put thereon is borne by the wire itself. When so mounted, solder is then placed around the physical connection to cement the electrical connection. This will lessen the chance of the wire coming loose again.

Sounds like the wire wasn't hot enough, or the tip of your iron has a lot of flux residue burned on it that needs to be cleaned off. The first iron I had, I completely ruined the tip because I was running it WAY too hot all the time, not keeping it properly tinned and cleaned, and it just turned black and nasty and would not heat ANYTHING other than to burn someone with. Soldering? Futile.

Once I got a new station, started using the tip cleaner metal scrubber thing and the wet sponge, much better results. I rarely EVER use separate flux now, as well, and when I do, VERY sparingly. Like literally I will use a toothpick and dab a tiny tiny bit. Solder can go bad after a while, but it takes a long time. I've never had that issue myself.

Also, Get some Tip Tinner/cleaner and a wet sponge (I use a copper pot scrubber) to clean off the tip before you solder. Soldering is all about heat transfer and if the tip of your iron is oxidized ie. crusty and dark, you need to clean it.

http://www.radioshack.com/radioshack-tip-tinner-and-cleaner-0-5-oz-/6400020.html

http://www.fleetfarm.com/detail/Quickie-2-Pk.-Copper-Mesh-Scourers

Wait for the iron to heat up and plunge the tip into the tip tinner/cleaner then wipe off the excess by dragging the tip across the damp sponge (or stabbing the pot scrubber). Before you attempt your solder connection, the tip of the iron should be silver and shiny, this helps the heat transfer from the iron to the part you are soldering. Sometimes I'll touch my solder to the tip to make a little ball and use that as my contact point to transfer the heat.

Tin your wires before soldering. Take your bare wire and hold it against the tip of the iron and touch your solder to it and it will wick up into your wire. This will make it easier when you go to solder your connection and you may not even need extra solder, just heat your wire and part until you see the solder look like the terminator from T2, once it's fluid and shiny remove the heat and hold until the solder goes solid. If the solder looks grey and dull when you are done, do it again. If it's shiny and chromelike, then you are good. Tug on the connection and make sure it's nice and solid.

There are alot of tutorials out there on the interwebs to help you out also. It's also a good idea to get yourself some old circuit boards and some scrap wire and practice wiring from one solder point to another on your scrap board.

EDIT: I never use flux unless I'm soldering to bare copper on a circuit board and I'm having issues with the solder sticking (it will ball up). I use flux core solder instead. I have maybe used flux twice in my life. I'm not saying don't use it, but I don't.

I prefer the solder sucker by a mile. Especially for coil lugs where you might be pulling off pounds of the stuff if someone got crazy with it. Just remember to prime it before you start heating up the lug, and don't be afraid to stick the tip right on the lug as you fire the sucker.

Mesh is good for circuitboards, but gotta be real careful with it...easy to pull a trace if it cools and adheres to a through hole. I still prefer the sucker on PCBs, personally.

You sound like me.

A thing I realized is that depending on the age, old solder had lead in it, and thus a higher melting point than whatever you recently bought. Adding new solder to old won't necessarily help it melt, instead you just get a hard glob of old solder on your new connection.

you have enough solder on the socket end of the bulb to re-use.

with the end of the wire that broke, you should strip it (twist the braids) and then "tin" it with solder ("tinning" is accomplished by feeding a bit of solder onto the exposed wire so that the wire takes on a [silver] appearance.

the "tinning" process also makes it easier to "bond" the wire with the lug. when you are applying heat, the tip of the soldering iron should touch the existing solder blob in this case, and by adding a small bit of solder from a roll, this will help initiate the process of melting the existing solder.

once the solder has melted, add the tinned section of the wire to the center of the solder blob and then pull away the iron, which should result in a good, solid bond

I have a WES51. If you had it turned up to 80, that's 800 degrees F. You'll destroy tips quickly running that hot. That iron takes all of 30 seconds to heat up and it is unnecessary to ever go past 70 ever (even with these large joints).

Anywhere between 65-70 is perfect. Make sure your iron is always tinned with solder too!

Sometimes the old wiring in pins is difficult to work with. Your best bet is to tin the wire first. Strip it, then hold the iron on the stripped end for several seconds and apply a small amount a solder. It may take a while (7-8 seconds even), but eventually it will tin. Once the wired is tinned, it will be about 100 times easier to solder it onto any existing joint. If you're having trouble getting the original solder joint to melt, try holding the iron more at an angle instead of 90 degrees so that more surface area touches it. That'll usually get it going after a few seconds. In these cases, I usually just get the desoldering vacuum and get rid of the blob and redo it.

And I've never once had any need to use flux, except for when I do SMD stuff with the liquid pen flux or I'm doing battery corrosion repair (again, liquid pen flux).

I'd also consider buying a soldering practice kit or an old board and practice a bit to get the confidence levels up. I've also noticed that desoldering is almost as hard as soldering is if you don't have the right tools, if you can afford it a good desoldering tool is worth it (e.g. Hakko 808)

(e.g. http://www.amazon.com/Velleman-MK130-3D-Xmas-Tree/dp/B0006HJSIW/ref=pd_sim_t_6 as the holidays are right around the corner)

the tinning process, as mentioned before, will help alot.

For desoldering, don't bother with those desoldering bulbs or hand vacs. They're garbage. The wick is the only inexpensive useful stuff (and only in certain situations). Otherwise, a desoldering station is the only way to go. I've repaired a lot more damaged boards from bad desoldering jobs than bad soldering jobs.

LOL, my soldapullt or whatever you want to call it cost all of 20 bucks and has seen me through three years of numerous board repairs, repins, a full Space Shuttle playfield swap (where every wire was cut, every coil, switch, and socket was cleared of old solder and resoldered anew), and a few other consumer electronics repairs. Knowledge is power, and a lot easier on your pocketbook than being lazy or ignorant. Agree that bulb-type suckers are crap, as are most of the hand vac types. The 808 might be the only exception to "hand held" that I would personally accept.

Otherwise. Spring loaded goodness SCHOOP, it's clean.

They're okay for some stuff. Not ideal when removing a 40-pin IC, and every time you miss or don't get it all removed, you have to reheat the pad, which is just excess stress on the solder pad.

When you can score used desoldering stations on eBay and elsewhere for under $100, it is a no brainer to pick one up rather than deal with the spring loaded vacuum.