In answer to your questions,
Remove the third lead, this will let you clear/prepare the pads for re-soldering.
It's probably best to flick the old solder off the leads; do this by heating and bending the lead with the tip of the iron and letting it spring back, DO NOT DO THIS TOWARDS YOUR FACE!
You can buy solder with a flux core. Also, if you can get it, buy lead solder, it is MUCH nicer to work with.
As regards the vid:
Yes the guy tins his iron to remove the leads, you should always tin (add solder to your iron tip) before you do anything, it stops the tip oxidising. It also helps when melting old solder.
To clean the pads generally I would put a bit of new solder on, then wick it off to give a nice clean and shiny surface.
He is applying flux, this will stop the solder "balling up" and sticking to stuff it shouldn't. You can do this, but if you are careful, and have flux core solder, you wont need to.
As regards the rest of your questions, this is just about technique. The guy seems to tack solder (a connection made to hold it in place) the leads at first. When the whole lead is tack soldered he goes around and tidies up the job.
So what YOU need to do.
Remove the lead - Tin and clean the pads and flick the old solder off the end of the lead (NOT TOWARDS YOUR FACE!)
Add a little solder to each of the pads
Place each lead above the pad and push down gently whilst touching the tip of the iron to the solder you placed on the pad. Make sure you remove the iron before removing the pressure.
When all connections are made, get some tweezers and push down on each lead in turn, melting the solder on the pad with the tip of the iron so the lead is properly flat on the pad.
Remember! Before you touch the iron to anything, make sure you have applied some solder to it and wiped it off on a sponge.
Also, if you are buying new equipment, when you first turn the iron on, keep adding solder to the tip and wiping it off. You need to thoroughly tin/protect the tip before you start using it. You can get little pots of hard flux, this is useful and it will help remove the crud on the tip due to oxidation. Also, tin it and DON'T wipe it off when you are done, the tip will still be hot for a while after you switch it off.
The iron you have should do the job if you use it once in a while. Although, if you plan to use if often, you should get a better one. It's worth it. The quality of the solder and flux also matter. All these will determine the quality of your work.
- Try a different solder. I purchased a chip one. It melted well, but I could not solder anything with it. Getting a more expensive solder worked well. Also, check out the metal composition ratio 60/40...??
- The tip of the iron might not be properly coated/wetted, so nothing sticks to it. When I had an iron similar to yours, I often had to scratch the surface of the tip with a fine file and use some solder and flux to coat the tip before soldering.
Best Answer
The transparent conductors are ITO (Indium Tin Oxide) deposited on glass. They're not easily solderable (perhaps possible with an ultrasonic soldering iron but even then they would likely be mechanically very weak).
You can use an elastomeric connector (zebra connector) as Dave Tweed suggests, but you'll need a closely matching pattern (preferably gold plated, or carbon printed) on a PCB.
It's also possible to use FPCs with conductive adhesive such as heat sealed types, but that's not practical for small quantities or one-off.
Silver-loaded or carbon loaded conductive paint might be a possible way to weakly attach to thin copper wires such as (stripped) AWG 36 magnet wire. I believe conductive paint is sold in auto shops for repairing heated car windows.