What Planck did to get the Planck length is a clever bit of calculation. Firstly he considered some fundamental constants of nature.
General relativity is concerned with two constants of nature: G (the gravitational constant, which determines the strength of gravity) and c (the speed of light).

Quantum field theory, on the other hand, is concerned with c (the speed of light) and h (Planck's constant, which determines the amount of uncertainty in our knowledge).

Physicists are attempting to unite these theories into one theory of quantum gravity. If this happens, we can expect all three of these constants (G, c and h) to play a role in the new theory.

Now note that:

The units of G are (distance * distance * distance) / (mass * time * time) The units of c are distance / time

The units of h are distance * distance * mass / time

Planck observed that there is only one way to combine these constants to obtain a distance:

Distance = square root (h*G/c*c*c)

The resulting distance is called the Planck length.