Those are good tips.
Solder type doesn't matter really, although I would opt for lead free. It takes a little more heat to melt, but a decent iron (~$20) will do the job.
If at least one of the two wires is still connected to the p-tap, you can tell your polarity. Some cables have flecks or stripes which indicate the positive wire. Some are red and black where black is your negative.
1 - remove the old solder. There are little air pump devices that can be used to suck up the old solder, just melt it and vacuum it up. It needn't be perfectly clean.
2 - prime the wire end. Clip the the "dirty" ends off, strip about 1/8" of the sleeve off. Twist the wires clockwise to make them compact, heat them with the iron, and melt a little solder onto them (separately).
3 - prime the terminal. Same deal, heat the contact on the p-tap where the wire connects and melt just a little solder on it.
4 - connect. Heat the contact area to liquify the solder on there, press the wire in and let it all melt together. It's important for the contact to be hot to avoid a "cold" joint (i.e., a bad connection).
Avoid using too much solder.
Although you need to get the metal hot for the solder to make a good connection, be careful not to melt the plastic parts of the connector.
P-taps are polarized as mentioned above, so just look on the connector for plus and minus.
If it's your first time, practice first. It's not complicated, but it takes practice.