It sounds like you don't have flux. It's a compound that you brush onto the wires that you need to solder.
The best way to solder is to strip and twist the wires together. Add a dab of organic, waterbased flux (it's made for electronics) to the joined wires. Take the iron, and melt off a bit of solder onto the tip, then touch it to the wire joint. The melted solder should flow immediately into the wires without much time/heating involved.
You can get this flux at RadioShack, I believe. There's also a brand called Sterling at Lowe's that's sold for plumbing, but is a waterbased flux as well. The organic waterbased is what you need. Some fluxes are clear liquid, and some are more of a creamy paste. I use a syringe to dispense mine onto the wires.
Acid based flux's are for plumbing, my can looks like earwax
, but it also comes available as a liquid that's brushed on.
While it will work with wiring, it will corrode the wires over time, and they will fail, usually up inside the insulation where the heat chased it to. Highly NOT recommended.
Plumbing solder is best left to plumbing.
Happy trails!
*edit* I take that back, the Sterling stuff turned copper green in a test I just did, so don't use it for electrical wires....