in c# how to program next letter in a word

You also need to allow for the possibility that the word might contain the letter 'z' or may contain characters which are not letters (e.g. hyphen or apostrophe).

In the former case, I suggest you 'wrap round' back to 'a' and in the latter case, leave the character unaltered:

using System;

class Program
{
   static void Main()
   {
       Console.Write("Input a word  : ");  
       string word = Console.ReadLine();
       char[] chars = word.ToCharArray();
       
       for(int i = 0; i < chars.Length; i++)
       {
          if (!Char.IsLetter(chars[i])) continue;
          if (chars[i] == 'z' || chars[i] == 'Z')
          {
             chars[i] = (char)(chars[i] - 25);;
          }
          else
          {
             chars[i] = (char)(chars[i] + 1);
          }
       }

       Console.WriteLine("The result is : {0}", new string(chars));
       Console.ReadKey();
   }
}

            string input = "cad";
            string output = "";
            foreach( char c in input)
            {
             int unicode = c;
             unicode++;
             output += char.ConvertFromUtf32(unicode);
            }
            Console.WriteLine(output);
            Console.ReadLine();