You can simply call the method .networkx_graph():
 sage: import networkx as nx
sage: G = graphs.PetersenGraph()             
sage: ng = G.networkx_graph()                
sage: ng
<networkx.classes.graph.Graph object at 0xd3c2f8c>
sage: nx.double_edge_swap(ng)                
1
 Incidentally, I didn't know this five minutes ago, so I should tell you how I found out.  Lots of functionality for Sage objects lives inside them, in methods.  Typically conversion functions are either called ".targettype" or "._targettype_", so I tried
 sage: G.netw[HERE I HIT TAB]
      G.networkx_graph
 which looked promising.  And then typing
 sage: G.networkx_graph?
 gives the documentation:
        Creates a new NetworkX graph from the Sage graph.
       INPUT:
       * "copy" - if False, and the underlying implementation is a
         NetworkX graph, then the actual object itself is returned.
       EXAMPLES:
          sage: G = graphs.TetrahedralGraph()
          sage: N = G.networkx_graph()
          sage: type(N)
          <class 'networkx.classes.graph.Graph'>
          sage: G = graphs.TetrahedralGraph()
          sage: G = Graph(G, implementation='networkx')
          sage: N = G.networkx_graph()
          sage: G._backend._nxg is N
          False
          sage: G = Graph(graphs.TetrahedralGraph(), implementation='networkx')
          sage: N = G.networkx_graph(copy=False)
          sage: G._backend._nxg is N
          True
 PS: Okay, to be perfectly honest, I tried it first and only looked at the documentation when I came to write this.  But I would've looked at the documentation if it hadn't worked, I promise!  :^)