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.

To show a grid line on every tick, add

plt.grid(True)

For example:

import matplotlib.pyplot as plt

points = [
    (0, 10),
    (10, 20),
    (20, 40),
    (60, 100),
]

x = list(map(lambda x: x[0], points))
y = list(map(lambda x: x[1], points))

plt.scatter(x, y)
plt.grid(True)

plt.show()

In addition, you might want to customize the styling (e.g. solid line instead of dashed line), add:

plt.rc('grid', linestyle="-", color='black')

For example:

import matplotlib.pyplot as plt

points = [
    (0, 10),
    (10, 20),
    (20, 40),
    (60, 100),
]

x = list(map(lambda x: x[0], points))
y = list(map(lambda x: x[1], points))

plt.rc('grid', linestyle="-", color='black')
plt.scatter(x, y)
plt.grid(True)

plt.show()

Using rcParams you can show grid very easily as follows

plt.rcParams['axes.facecolor'] = 'white'
plt.rcParams['axes.edgecolor'] = 'white'
plt.rcParams['axes.grid'] = True
plt.rcParams['grid.alpha'] = 1
plt.rcParams['grid.color'] = "#cccccc"

If grid is not showing even after changing these parameters then use

plt.grid(True)

before calling

plt.show()