String has a Contains method that should suffice, returns a boolean
"Big string that represents a paragraph".Contains("that");
Example from the Contains Method MSDN page:
// This example demonstrates the String.Contains() method
using System;
class Sample 
{
    public static void Main() 
    {
    string s1 = "The quick brown fox jumps over the lazy dog";
    string s2 = "fox";
    bool b;
    b = s1.Contains(s2);
    Console.WriteLine("Is the string, s2, in the string, s1?: {0}", b);
    }
}
/*
This example produces the following results:
Is the string, s2, in the string, s1?: True
*/
If you need more advanced matching then Regex might be the correct route, but from the example you stated I think contains will work fine.