As obvious as it sounds, you just need to practice if at all possible. The main reason I signed up for the Etape last year was because I had qualified for Nice and I wanted to get more experience both climbing and descending. It made a massive difference. Just a couple of days of big mountains out in the Alpes and I felt so confident around Nice. I also got there early and rode the course on the Tuesday before.
The other thing is having the course map on your bike computer. This was a tip given to me by a KQ from our club. Again, makes a massive difference. Knowing a corner is just a little kink rather than a hairpin has made me a lot more confident. Knowledge is power, etc. I only use the map on descents. And as I use a BBS power plan, the route is already loaded up anyway.
I know that’s more about myself rather than passing others, but as Matt says, if you can take corners more effectively, then you can actually pass people on the safer straight bits by carrying more speed out of a corner. Rather than in the hairpin itself. As he says, and a bit like F1, brake early and accelerate out