tl/dr: just add with_labels=True
to the nx.draw
call.
The page you were looking at is somewhat complex because it shows how to set lots of different things as the labels, how to give different nodes different colors, and how to provide carefully control node positions. So there's a lot going on.
However, it appears you just want each node to use its own name, and you're happy with the default color and default position. So
import networkx as nx
import pylab as plt
G=nx.Graph()
# Add nodes and edges
G.add_edge("Node1", "Node2")
nx.draw(G, with_labels = True)
plt.savefig('labels.png')
If you wanted to do something so that the node labels were different you could send a dict as an argument. So for example,
labeldict = {}
labeldict["Node1"] = "shopkeeper"
labeldict["Node2"] = "angry man with parrot"
nx.draw(G, labels=labeldict, with_labels = True)
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