Step 2: Step 1 of Cutting the Bottle - Scoring the Bottle
Use the glass cutter to EVENLY score a constant line around the entire circumference of the bottle. If the score line is spiraling (moving along the circumference of the bottle at an angle) then when you later apply stress to the score line you may have imperfect cuts.
The tutorial mentioned earlier, like many others, notes that the score line should not be too deep. I personally found that giving a second go around the bottle resulted in greater consistency in clean cuts - maybe i was lucky, maybe there is something in it. I recon there are too many variables to say definitely whats best every time which is why i recommend practice a few times with the type of bottle you intend to cut first!
Your accuracy will depend somewhat on the glass cutter you use. The cheap ones off ebay (which work just fine!) are handheld - essentially a sharp disk on the end of a stick, and so you will need to be inventive with how you make sure the cut is even, You could use tape to mark where you will cut, or draw a line with a permanent marker on the bottle, whatever works for you.
I used a cutter which is on the end of a jig (see picture) and this made things a bit easier - but the principle is the same and can just as easily be forgotten. Even cuts. Practice first.
Safety. Probably a good idea to wear some goggles or glasses just in case a stray bit of glass defeats the odds and makes it anywhere near your eyes. Its unlikely, but worth mentioning.