Soldering
Few things right off the bat -
1. Get a sponge and get it wet. Place the sponge in a bowl with a little water so it stays wet. This sponge is to clean the tip so it does not keep 'gunking' up between solders and tinning.
2. Is the solder you are using "lead free" or "silver"? If it is, put it away and go get some
LEAD 60/40 solder (or LEAD 63/37 which goes back to solid almost instantly while 60/40 can take a second or three). (Why? Because the no-lead stuff requires a lot more heat to go from solid to liquid.)
3. The object is to get the two things you want to solder hot, not the actual solder. I am hoping your Weller is at least 25 watts and not greater than 35 watts because inside that range, the rail and the wire should heat up enough to touch the solder to them in less than 15-20 seconds.
4. Once you get past connecting stuff, work on getting the solder to look shiny when it cools. If it looks cloudy or dull, it may not conduct electricity well and is a brittle solder joint.
I am looking around for a link with pictures and "How to..." but in the meantime, here is what you should end up with:
*Sigh* The only videos for soldering models are trying to sell me something to solder with, so this is the best thing I could find with decent pictures:
How To Solder