Edit
I am adding new headings for each section of possible solutions.
Centrifugal Force
Suppose that the planet is not revolving at all then the effect of gravity can be reduced by moving around the planet in a high speed train (assuming that by reducing the effect of gravity you mean the measured weight).
How?
When you move with speed $v$ around the planet then the forces acting on you are gravitational force $F_g$ and normal force $\mathcal N$ (neglecting the dissipative forces).
$$\Rightarrow \mathcal N - F_g = - m \frac {v^2}{R}$$
i.e.,
$$ \mathcal N = F_g - m \frac {v^2}{R}$$
Here $\mathcal N$ is what you measure as the effective gravity ($R$ is the radius of the planet).
Similarly if the planet is rotating then you can reduce the effect of gravity by moving in the direction of rotation of the planet.
Free Fall
Other option is to use the concept of free-fall:
place the stuff, on which you want to reduce the effect of gravity, in orbit around the planet (this will completely eliminate the effect of gravity) and then if neccessary increase induce some artificial gravity.
alternatively, 0-gravity planes(Reduced Gravity Aircrafts) are now available, and you can book tickets for them and experience reduced gravity.
Shell Theorem
Shell Theorem can be quite useful in reducing the effect of gravity. It states:
If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.
This means that if you are inside a well then the shell of earth above you applies no gravitational force on you (obviously this is base on the assumption that planet's density is uniform).
So you can build some structure underground, in mines (...,etc), and reduce the effect of gravity on yourself.