How is mining of bitcoins done What makes this mining process so computationally intensive and can this mining activity be substituted by other hard labors in physical world?
Does this mining effort alone adds intrinsic value to the bitcoin like gold?
The mining process is similar to a brute force attack and, assuming you already appreciate the nature of such attacks, mining is computationally intensive.  More specifically, mining involves repeatedly, and as fast as your computer allows, guessing at the solution to a problem that cannot be solved quickly by the human brain.  There are now dedicated computers, made specifically for the Bitcoin community, able to make billions of guesses per second.

The mining process is hard by design as it does make the Bitcoin generation process harder, almost like mining for gold.

The mining activity cannot be substituted by other hard labors in the physical world.  BUT, you can buy Bitcoins on an exchange with the dollars you earned in the physical world.