Summarize:

If your core is round or has an irregular surface, you'll need to strike it with a hammerstone to create a relatively flat "platform" to start with. The stone will fracture at roughly a 50º angle from the direction of impact, so for a round rock you'll want to tilt the core to about 40º and strike straight downward. The platform must be next to a side that narrows inward. You won't be able to use any side that bulges outward from the platform, or goes straight down at a 90º angle. If you are using a core, once you have a flat platform, use your hammerstone or billet to strike off flakes, or thin, relatively flat pieces you can turn into tools. Always remember that the stone fractures at a 50º from the point of impact. To use this to your advantage, tilt the core so the platform is at a 40º angle from the vertical. Strike the lower end of the platform with the tool, hitting it with a glancing blow that carries on past the point. You may need to repeat this several times around the platform, until you get a piece that is mostly flat, and a fair amount larger than the tool you want to make.  If the material splits into three pieces, or the platform crumbles around the blow, the angle is probably too small (the blow is too direct). If you're only getting tiny chips, the angle is probably too large (the blow is too glancing). Unless you were lucky enough to get a perfect triangular or rectangular flake, you'll probably need to break it further. Do this using the same direct percussion technique, until you have a piece a bit larger than what you want to end up with, and with no concave "bites" taken out of the edge. Abrading is one of the most important processes in flint knapping. A newly struck flake typically has thin, fragile areas around the edge, which need to be ground down to a dull, thicker edge so it can withstand the impact of the tool. To accomplish this, grind the edge of your flake in a sawing motion against another flattish sort of stone of slightly lesser hardness. Old grinding wheels work well for this, or any smooth hunk of limestone. If grooves appear in the tool you are grinding with, this is a good sign, since it means the tool is softer than the flake. Once the fragile edges have chipped off or been ground down, you'll have a dependable platform able to take the extreme rigors of lithic engineering.
Create a flat platform on the core (if necessary). Use direct percussion to create flakes (if necessary). Trim the flake shape. Abrade the edge of the flake.