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

You want to use pyplot.grid:

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.grid()
plt.show()

ax.xaxis.grid and ax.yaxis.grid can control grid lines properties.