You apply heat to both the pad and the pin at the same time. Touch the solder in amongst it amongst it all and allow the joint to heat up just enough to cause the solder to flow into the joint. You want to tread the fine line between starving the joint and creating a huge blob that might even connect to the adjacent pad/pins.
Look at solder joints on a variety of boards and you will have examples of how it should look when you get done.
I'm not sure about the lead-free solder. Haven't used. For the regular stuff, I have used 0000 steel wool to clean a cruddy tip and have always had good tinning of the tip. If you have an extra tip and don't mind possibly ruining one, you could try it.
Weller is a good brand. Mine is a cheap POS, but it works for my limited use. I had a computer repair business. When it closed, the technicians stole all the good equipment. I don't think they were worried about being fired for it.
John