Conditional compilation is all driven from compiler preprocessor definitions. This is the same approach used for the DEBUG constant, although Visual Studio hides the definition of that behind a checkbox. It's an efficient approach because when those symbols aren't defined then the methods aren't called at all; importantly the parameters being passed aren't evaluated either, so you can use relatively expensive checks in your code contracts without worrying about those checks slowing down release builds.
Microsoft's introduction to Code Contracts says this:
Most methods in the contract class are conditionally compiled; that is, the compiler emits calls to these methods only when you define a special symbol, CONTRACTS_FULL, by using the #define directive. CONTRACTS_FULL lets you write contracts in your code without using #ifdef directives; you can produce different builds, some with contracts, and some without.
Although this talks about using #define in the code to turn on code contracts:
#define CONTRACTS_FULL
as @NirMH said in the comments it's usually better to define it in the conditional compilation symbols for the project so you can have it on for some builds and off for others.
Note that CONTRACTS_FULL is the only option you have, although it's clearly been named to allow the possibility of more granular control in future.
