Well, as an ex Draughtsman, albeit of 25 years ago, I may be able to assist!
Firstly, you do need a reasonable quality pencil! Most pencil manufacturers make a range of qualities, and any of the top end will be more than adequate!
If you'd like some names, we're talking Staedtler Mars Lumograph, Faber Castell 9000, Rexel Cumberland Graphic, Caran D'ache Technograph, Tombow Mono and Mitsubishi Hi Uni!
The last 3 are a bit specialised, and probably overkill, but any of the former are fine! I have to say that I use the much cheaper Staedtler Noris in the workshop without problems, but the leads are harder to sharpen!
To sharpen, always use a really sharp knife, rather than a sharpener. That way you cut along the grain of the wood, rather than across. The traditional 'penknife' is perfect, alternatively, so is a decent scalpel!
With a soft lead, say B or softer, just sharpen the lead with the knife! Cut at a shallow angle and slowly (speed comes with practice) and pull the knife as you cut so you are sawing rather than just pushing like a razor! Decent pencil and a little practice and you will be fine! If you are constantly breaking the lead it usually means you are trying to cut at too step an angle, or the knife is blunt!
For finer points with harder leads (say 2H and harder) remove some of the wood first so a little of the lead is sticking out like a propelling pencil, then sharpen using a rotary motion on some really fine sandpaper! Between the grades, use whichever method works!
Alternatively, for more durability, get a proper carpenters pencil. Sharpen to a chisel point by removing a little wood then sharpening on sandpaper to a chisel shape. These work well for carpentry (Unsurprising!) but again you need a decent quality and I see a lot that are not. Here on the U.K. I use Rexel, but I don't know how available these are in the U.S. !