You can pick up 25 watt and 40 watt soldering irons at places like Princess Auto for around $6 - $8 each. I have about half a dozen of them and they work very well for soldering rail joiners, soldering 20AWG track feeders to 16AWG track power busses (I use DCC). The trick for any soldering iron is to make sure it heats up to its maximum. If the solder melts immediately when touched to the tip of the iron, then it's hot.
For ease of use, get a holder to hold the soldering iron in. The commercial ones are usually a large " coil spring-like" contraption that is screwed to a 4"x 6" metal base. The metal base has a depression to fit a small 2"x 3" sponge. Or, if you don't have something like that, then take a clean empty small tin, like a cat food tin, cut out a couple of notches so that the iron will fit on the top of the can but not roll off.
Before you solder any rail joiners or pieces of wire, apply some flux to the joints - even though the solder may say it is "flux core" solder. There isn't enough flux in the centre of the solder to spread the flux on the work to be soldered. Flux comes in a paste form or a liquid form. Only a little bit of flux is required - a bit of paste on the end of a toothpick will do. Or, dip the ends of the wires into the paste. For liquid flux, a small micro-brush will do, or even that toothpick.
Before applying the hot iron to the work to be soldered, wipe the tip of the iron off on a dampened sponge or a damp piece of cloth. As the iron continues to heat up, the tip of the iron will oxidize. You know the tip is cleaned off if you can see the silver of the solder. I presume you know how to tin a new soldering iron so I won't get into that here.
With the flux applied to the parts, place your hot iron onto the parts to be soldered. Start counting - one thousand, two thousand, three thousand, four thousand. At the count of "one thousand", apply your solder. If the solder hasn't flowed into the joints/ wire at the end of "four thousand", immediately remove your soldering iron. The plastic ties on your rails (or the plastic sheathing on the wire) will start to melt.
Keep your eye on the plastic ties. The minute they start to seem as if they are soft, immediately remove the soldering iron. Practice first on a piece of scrap track or wire.
The key here is a hot iron, a clean iron, parts that have been fluxed. Apply the heat and the solder fast. Get in, get out, fast! Make sure the solder "flows". Solder that doesn't flow results in a "cold" joint that will cause electrical conductivity problems.
Bob M.