Microchip application note AN513 describes a method for ADC.
I'm not that great at analog electronics, and I don't quite understand the
schematics. It has this chip that is supposed to be voltage to current
converter 4066, but according to my data it is a quad bilateral analog
switch. How could it convert anything?

I'll try to reproduce a part of the schematic here:

     S1
 1 /----\ 2
---| 13 |----+
   \----/    |
             |
 4 /----\ 3  | 5  |\ 4066
---|  5 |----+----|+ \------
   \----/      +--|- /
     S2        |6 |/
               |
               |

I don't quite understand what those S1 and S2 things are.

Thanks for your assistance.