How do I increment letters in c++?

It works as-is, but because the addition promotes the expression to int you want to cast it back to char again so that your IOStream renders it as a character rather than a number:

int main() {
   char letter[] = "a";
   cout << static_cast<char>(letter[0] + 1);
}

Output: b

Also add wrap-around logic (so that when letter[0] is z, you set to a rather than incrementing), and consider case.

This snippet should get you started. letter is a char and not an array of chars nor a string.

The static_cast ensures the result of 'a' + 1 is treated as a char.

> cat caesar.cpp          
#include <iostream>

int main()
{
    char letter = 'a';
    std::cout << static_cast<char>(letter + 1) << std::endl;
}

> g++ caesar.cpp -o caesar
> ./caesar                
b

Watch out when you get to 'z' (or 'Z'!) and good luck!