Am I doing something wrong when I solder?

I am not exactly sure what I am doing wrong, or if I am even doing anything wrong when I solder. I have a Weller WES51 with a PES51 pencil, and the tip that comes with it. I usually have the station set to between 500-600 degrees fahrenheit, and I believe my soldering procedure is correct. I make the tip contact both things I am soldering together, and apply the solder to the other side of the joint. I pull both the tip and solder away when there is enough solder on the joint, and it has flowed smoothly. I don't own separate flux, but I do have multi-core solder. This is what I am worried about:

Is that black supposed to be there? Does the tip look tinned to you? The solder I am using was my fathers when he was in college about 25 years ago, could that be the problem? This is the solder:

I have only used this soldering equipment 3 times and I don't want it to deteriorate faster than it needs to.

Also if you can't tell, I am extremely inexperienced. This year as a Junior in high school has been my first step into electronics as a hobby, and I want to make sure I am at least attempting to do things the right way from the beginning.

Hey man, no problem, we all start somewhere. That black is pretty normal. You can clean it with 60 grit sandpaper after it is cool and that works pretty well. A lot of people do not heat the object they are soldering first, that can weaken joints. you simply heat up your iron, then heat up the object that you intend to apply solder to, then apply solder to the heated area via the iron. clean iron tip with moist sponge from time to time and allow to reheat. THe ago of the solder should not make much of a difference. 60/40 rosin core is what I use on guitar wring harnesses. It is quite heavy.
also, dont "blow" your joints cool. It makes them brittle. from what it looks like to me, you may want to tin the tip a bit better though.
But the number one rule of soldering is to keep a clean iron. not only will a dirty iron ruin it, it makes it heat up slower and not get as hot. both bad things.