How do I draw a grid onto a plot in Python?

I just finished writing code to make a plot using pylab in Python and now I would like to superimpose a grid of 10×10 onto the scatter plot. How do I do that?

My current code is the following:

x = numpy.arange(0, 1, 0.05)
y = numpy.power(x, 2)

fig = plt.figure()
ax = fig.gca()
ax.set_xticks(numpy.arange(0, 1, 0.1))
ax.set_yticks(numpy.arange(0, 1., 0.1))
plt.scatter(x, y)
plt.show()

And its output is:

What I would like is the following output:

EDIT: Added an exemple, based on Andrey Sobolev’s answer