Soldering is easy. Two things are important... keep it hot...keep it clean...I use a Weller solder gun for car wiring, there are cheaper makes that will be fine if you are only doing the odd job I found one on Ebay item #300014463709 for £10.
Use 60/40 multi core solder. (this has the flux which cleans the joint, inside the fine holes that run inside the solder)
To make a splice joint, strip back the insulation and wrap the wires you want to join together. pull the trigger on the gun, it takes about 15 seconds to get up to full heat, then apply THE TIP OF THE GUN to the joint. You will see the joint start to heat up as the insulation will start to melt. Apply the solder wire (which has the flux inside it) to the tip and the joint. and as soon as it flows evenly remove the heat and the job is done. Wait for it to cool and wrap with tape or heatshrink...Job done.
WARNING dont put the gun down on the carpets in your car, it takes a while to cool down.
Dont work upside down under the dash soldering. Hot solder dripping on seats and carpets is not funny and dropping in your eyes has the same effect as self abuse !!!!
Do NOT use a gas iron, blow torch thermal lance or log fire unless you have a lot of experience as it will end in tears.
Invest in the solder gun, P-R-A-C-T-I-C-E on odd bits of wire and when you get it right all your mates will want to buy you pints for doing their soldering...Gun paid for !!!!