Soldering Connections on alarm/remote st

I have a question on this.  Being in the process of installing an alarm and having problems with my 30 watt soldering wand not heating up the ignition wires enough to melt the solder with the wire...  I used an alternate method:  I used the solder iron to melt the solder under the wire (holding the solder iron under the wire, touching it).  The solder would melt and absorb into the wire, but only about half way up.  I held the solder iron in contact with the wire for quite awhile until I started smelling the wire shielding "cooking" and then would give up.  Later I came back and twisted the wire upside down and performed the same proceedure on the top, but didn't feel comfortable with this method being "correct".

Any solder "masters" care to eleborate on some of the potential problems that might be experienced while trying to solder and any definite do's and dont's to keep in mind while soldering?

Thanks,

Bret