I am going to explain one of the common approaches used to create URL shortner.

1. Think of an alphabet we want to use. In your case that’s [a-zA-Z0-9]. It contains 62 letters.
2. Take an auto-generated, unique numerical key (the auto-incremented id of a MySQL table for example).

   For this example I will use 125₁₀ (125 with a base of 10).

3. Now you have to convert 125₁₀ to X₆₂ (base 62).

   125₁₀ = 2×62¹ + 1×62⁰ = [2,1]

   Now map the indices 2 and 1 to your alphabet. This is how your mapping (with an array for example) could look like:

   0  → a
   1  → b
   ...
   25 → z
   ...
   52 → 0
   61 → 9
   

   With 2 → c and 1 → b you will receive cb₆₂ as the shortened URL.

   http://shor.ty/cb
   

How to resolve a shortened URL to the initial ID

The reverse is even easier. You just do a reverse lookup in your alphabet.

1. e9a₆₂ will be resolved to “4th, 61st, and 0th letter in alphabet”.

   e9a₆₂ = [4,61,0] = 4×62² + 61×62¹ + 0×62⁰ = 19158₁₀

2. Now find your database-record with WHERE id = 19158 and do the redirect.