The Library of Congress site contains gems like this map showing the proposed final link of the original world wide web: the proposed trans-Pacific telegraph line, envisioned with Civil War-era technology.
Thirty years later, Britain's All Red Line was working to connect the entire British Empire:
At the same time, the Commercial Pacific Cable Company also began making the dream a reality.
Below are a couple of articles about the process, including images of the equipment used.
• The Commercial Pacific Cable Company
• The Laying of the American Trans-Pacific Cable (1902 article)
Here's a current map of submarine cables.