Specific solder wire/flux questions
It looks like you have already got some good answers, but I'll add some basic points that helped me when I was having trouble soldering.

1) Solder flows towards heat.  That is why you heat up both components and then add solder.

2) Flux helps the solder to flow to where you want it.  Even if the solder has flux in it, if you are having troubles, try using flux.

3) 2 main types of flux: Acid and Rosin.  Only use rosin for electronics, use acid when plumbing your toilet.

4) "Tinning the tip" adding a little solder to the tip of the soldering iron before you start to heat up the components you are going to solder helps to conduct the heat to the components and just makes it work better.

5) Using the right tip- I couldn't believe how switching to a chisel tip helped me for one specific application that I just couldn't do with the pencil tip that came with the iron.

6) Don't Move! Hold still while the solder hardens. This will only be a second or two or even less depending on the solder.  A "cold joint" could form if you move the components as the solder is cooling. Cold joints are unstable and likely to cause you future problems

7) Ventilation - Lead is bad for you.  Your soldering iron should not be hot enough to vaporize lead, but the flux does create some smoke which has possibly been linked to asthma in factory workers.

Hope this helps.