Even among the electronic grade rosins, some are acidic and need to be washed away with water. You can't use these for wires, because they'll wick up into the wire and cause corrosion. Others can be left in place or washed away with alcohol. These can be used on wires and parts that can't be washed. There's a lot of different fluxes out there from different manufacturers and/or different scenarios.
Apply the flux first, then the soldering tip, then the wire solder. Generally, you want to apply the tip to the board and component at the same time to heat both up. If one part is a much more massive heat sink than the other, you may need to heat that part up first, so you don't melt the smaller part.
If you are joining wires, tin both ends separately. I normally don't add extra flux to wires, other than what is in the wire solder. If it's an old corroded wire, you might need to add some flux. Once both ends are tinned, use three hands (j/k) to hold the wires adjacent, then heat them up with the soldering iron together. When the the solder melts together, remove the iron and continue to hold them together until the solder hardens.
With braided wire, you want to be fairly quick, otherwise you'll heat the wire up under the insulation. The hot wire can melt the insulation and/or wick solder up under the insulation. That can create a breaking point if the wire moves around the point where the solder stops.
If you're having a lot of problems, practice getting the rhythm down. It's a lot about timing. If you're still having issues, maybe try a different iron or tip if it can be replaced. Also, use a 37/63 tin/lead solder. It's much easier to work with than the lead-free varieties, as it melts at a lower temperature and behaves better.