'...the company Field founded' = the company that Mr. Field brought into existence ('to found' is a verb in itself, not just the past of 'to find') 'set out to lay the cable...' = began to lay the cable Therefore, the sentence means that the company that Mr. Field brought into existence began to lay the cable....

Sheena's answer is excellent. There are two ideas here: "the company set out to lay a cable" and "the company that Field had founded." There may be a copying error in the text. Original - In 1857, the company Field founded set out to lay the cable that has taken months and almost a million dollars to make. Correction - "has taken" > "HAD taken" In 1857, the company Field founded set out to lay the cable that HAD taken months and almost a million dollars to make. Elaboration - In 1857, the company [THAT Field HAD founded] set out to lay the cable that HAD taken months and almost a million dollars to make.