I have a board I ripped out of a very old phone to practice on :)
That's good - practice on it; learn to desolder parts, solder them back in, and solder wires to points (hint: tin the end of the wire first, then solder the tinned wire to the point on the board - if the wire is stranded, after stripping the insulation, twist the strands up tight, then tin the wire end - it will soak it up fairly easily. Once it is cooled, snip off the very tip if there is any excess or extra strands sticking out).
You might also practice making solder bridges between close pads and cleaning them up - this is just something you need to learn, because you -will- make them, and understanding how to clean up a bridge (or make one!) is important. Bridges are made best when the pads are close together, but if the pads are too far apart, you may need to use a piece of thin wire (solid core works best). Surface tension is the key to all soldering; you heat the solder on the pad up (until it is shiny), and if the pad is close to another, the idea is to heat both together and "shove" them together so they form a joint bridge. Then let them cool (don't leave the heat on too long, or blow on the hot solder to cool it too quick, just let it naturally cool - otherwise you run a risk of a "cold joint", which is weak and may be electrically unsound. If you have to use a piece of wire, tin it first, then heat up the pads (you have to be quick - though sometimes you might just need to do one, then do the other, and let the heat flow thru the wire to keep the other end fluid), and shove the wire around until it fits and the solder flows over it, then let it cool. It will take some practice, but you'll get it.
Your first thing though is to learn to desolder parts and solder wires - because that is what you'll need to do on this PCB. You'll solder the wires first, probe around, then once you have everything situated (and label the wires!), you can desolder the IC; desoldering DIP ICs is tricky, though. You'll quickly run out of hands (if you have a vice or can improvise something, it will help). The best way is to use a combination of a solder sucker and desoldering braid to remove most of the solder off the pads (you won't be able to get it all). Then with a small screwdriver under one end, you carefully pry on the IC (not too much force!) while reheating the pins, and "pop" the pins off. Don't spend too much time on any one pad; if it ain't working, move on to the next, and let it cool down; you don't want to lift the pads if you can help it (but it will happen occasionally). If it really isn't working, the move of last resort is to use wire dikes to cut the pins from the IC body (this renders the IC useless, btw), then desolder the pins one-by-one from the board.
Here is the new diagram
That looks perfect!
Also on the solder points are spots B and C acceptable or do I need to be going over the previous solder point like A?
You want to solder on pads away from the main pads holding the IC on - because later you will desolder the IC, and you don't want your wires falling off, right? That means the one underneath "B" is most acceptable, and the one on the other end of "C" would be better. Only solder on to the IC pad if you have no other choice (like for instance, you are using a function that the pad represents that -wasn't- brought out on the board), or if you aren't desoldering the IC. You'll know when you need to do what.
You said "You want to solder to that resistor anyway to limit current to the transistor's base - whatever you do, don't solder to the base of the transistor, as you may end up drawing too much current and burn out either the resistor (or the Arduino's port)."
Where am i meant to put resistors and what value? or do you mean I should trace it out to the resister and solder to the resistor rather than one of the points off the chip?
Well - first try to locate the resistors; if you follow the traces from the pads for pins 6 & 7 (right/left) and 10 & 11 (backward/forward), you should end up at a resistor pin (if the manufacturer followed the reference diagram in the datasheet - or something like it). If you end up at a transistor pin, then the manufacturer was flying fast and loose, and you should add a resistor; use the values as given on the datasheet, which is 690 ohms (or something close if you don't have this value). Either way, you want to solder your wire to that pin, and not the IC pin (and remember, the further you can get away from the IC and closer to the h-bridge driver circuit, the better).
Also - once you have your wires in place, and you know their function (and you know they are soldered on good), put a dab of hot glue on and around the joint to provide some "strain relief" so they don't pull off as you experiment. Hot glue is non-conductive, so it won't be a problem.
Finally - may I use your photographs and such that you have posted here for use in an article I want to write up on my website? They are fairly clear, and would save me some time and effort. I think all of this that I have written could be useful to others in the future...