On the other hand...
I never use flux, but I use a rosin core solder. Drilling a hole through the PCB should help things a bit. It's ten times more difficult to solder a wire held against the side of a contact than it is to pop it up through a hole surrounded by copper. Just make sure it's BARE copper that has been scraped clear of any protective covering. And check the other side of the board to make sure that no circuit traces run thru the spot you'll drill (these should be readily visible at the surface.) Make the hole with a small drill bit or by twisting the tip of a hobby knife.
In my opinion, there are 6 essential tools for soldering projects. 1) A good soldering iron with a pointed tip. 2) rosin core solder. 3) Soldering tin! This is necessary to keep your tip from corroding, as well as facilitating the transfer of heat to your joint. 4) A set of "extra hands". You've probably seen this around Radio Shack, it's a set of alligator clips and a magnifying glass clamped to a weighted base. The clips hold your work while you hold the iron and feed the solder. A real time saver, which means you're less likely to melt your components, or your flesh! 5) A clip-on heat sink. This is a must when soldering on (or close to) sensitive components. Literally draws the heat away from the contact, so you have more time to solder before meltdown!
6) A copper desoldering braid. This stuff is dirt cheap and will save your life when you inevitably splatter a gob of solder across your PCB! Also handy when you need to remove a component from the board.
All of these tools will help make your soldering easier, safer, and more permanent. Once you learn the proper technique and assemble the necessary tools, you'll turn endless hours of solder-dropping, rug-burning, board-melting, flesh-searing frustration into quick, one-minute, professional-looking, works-like-a-charm solder jobs. Trust me, I used to be the world's sloppiest (and most dangerous) soldering hack!
Allow your soldering iron a couple of minutes to really heat up after plugging in. When soldering, you first place the wire or component lead onto the contact to be soldered, preferably thru a hole in the copper. Use your "extra hands" (or an alligator clip or clothespin) to hold the two together. Touch the tinned tip of your iron to both the contact and the wire, holding it at a 45 degree angle to the board (for better heat transfer.) If you're doing it right, it should only take a second or two to heat it enough that you can feed the solder. Touch the solder to the contact and wire until it melts enough to cover the joint between the two. Quickly withdraw the solder and iron, and hold the wire still for a few seconds while the solder cools. You should have a nice, neat connection when you're finished. Piece of cake!
BTW, solid core wire works much better than stranded wire. It heats up quicker and stays put while soldering. If you're using stranded wire, twist the end together and coat it with some solder. This is called "tinning", and will keep the wire from fraying while you work with it, and makes it bond with the solder more readily.
Lastly, make sure you're not using headphone wire or something. This stuff seems to be coated with something to make it more flexible, and is just about impossible to get a good joint with. It actually seems to repel the solder! I recommend 22 AWG solid core wire for both PCB soldering and general control panel wiring.
Good luck!