How do I plot Shapely polygons and objects using Matplotlib?

Use:

import matplotlib.pyplot as plt

x,y = polygon1.exterior.xy
plt.plot(x,y)

Or, more succinctly:

plt.plot(*polygon1.exterior.xy)

A little late but I find the most convenient way to do this is with Geopandas as suggested above but without writing to a file first.

from shapely.geometry import Polygon
import matplotlib.pyplot as plt
import geopandas as gpd

polygon1 = Polygon([(0,5),
                    (1,1),
                    (3,0),
                    ])

 p = gpd.GeoSeries(polygon1)
 p.plot()
 plt.show()

Checkout the docs for Geopandas.GeoSeries

If your data is in a .shp file, I would recommend geopandas:

import geopandas as gpd
import matplotlib.pyplot as plt

shapefile = gpd.read_file("path/to/shapes.shp")
shapefile.plot()
plt.show()

It might be an overkill, but as an alternative to other good comments I would add an option of installing QGIS - a free software for working with geometries. All you need to do is to save your geometries as a shape file (.shp), geoJSON or any other format and open it with QGIS. If you're planning a big project it maybe more convenient at the end than using matplotlib.