I'm exploring the history of the Peloponnesian War and I was wondering how much money a trireme cost and how long it took on average to build such a ship.
Two talents may confidently be assumed, [...] as a moderate estimate of the cost of both hull and rigging of a trireme. (p. 364)
Newer authors (relying, as far as I can tell from a very cursory examination, upon basically the same literary sources as Robbins and his authorities) seem to stay in the same ballpark.
An Attic talent was equal to 6000 drachmas and since wiki tells us that, "According to wage rates from 377 BC, a talent was the value of nine man-years of skilled work.", this tallies quite well with the answer given by @Pieter Geerkens.
Wikipedia, after Hanson (2006), claims that a typical trireme took 6,000 man days to complete. If you take a 25 man crew as around the optimal size, balancing the ease of performing certain tasks against the non-linear aspects of managing large teams, that would equate to 240 days effort, or perhaps 9 months elapsed time allowing for days off, bad weather, etc.
Certainly one single trireme could be built faster with a larger crew, at the cost of efficiency, but to construct a fleet one would desire to have the optimal crew size working on each ship. The quality of the finished vessel would be affected by whether or not the wood had been seasoned a full two years before construction started.
As has been stated also by others, the real cost of a navy was not the construction cost, but the operating cost. According to Thucydides, the operating cost in 5th century Athens amounted to one silver talent per trireme per month, which is approximately 25 kilograms of silver per month.
This is mentioned in Thucydides VI, 8.1 when in the spring of 415, Athenian envoys, together with Egestean representatives returned from Sicily bringing 60 talents of silver for one months pay to 60 Athenian triremes (ἑξήκοντα τάλαντα ἀσήμου ἀργυρίου ὡς ἐς ἑξήκοντα ναῦς μηνὸς μισθόν).
When describing the Athenian fleet about to embark on the major Sicilian expedition, Thucydides VI, 31.3 explicitly mentions that the daily wage paid by the Athenian state to each seaman amounted one (silver) drachma (τοῦ μὲν δημοσίου δραχμὴν τῆς ἡμέρας τῷ ναύτῃ ἑκάστῳ διδόντος). This squares nicely with the overall monthly cost of one talent per trireme per month, considering that each trireme had a crew of approximately 200 and that one talent = 6,000 drachmas.
Please bear in mind that Thucydides was himself (if only briefly) an Athenian general during the Peloponnesian War in command of a small fleet of triremes, so his testimony is as reliable as one could hope for.
I have found the BA dissertation by Rosemary Peck to provide good discussion and an excellent collection of additional reading on this subject.
The common consensus by both ancient writers and modern is that it took about 1-2 talents of silver to field a ship.
However, the operational costs of a ship were generally greatly in excess of the costs just to build it.
For example, in the Samian War the Athenians demanded an indemnity of 1300 talents to re-imburse them for the costs of the war and the Athenians fielded 60 ships for 9 months in that war. So, that would be at least 20 talents per year per ship. This would indicate the operational costs were a lot higher than the ship building costs.
A silver talent equates to roughly $750,000 now in wage earning power.
For example, a 150-200 man crew of a trireme might be paid 1 talent per month. So, at $750,000 per talent that would be $3,750 per month per man or $45,000 per year which is about what the average Navy sailor makes right now.
Thus, the modern equivalent of the 60-ship Samian war would be 1300 x $750,000 = $9.75 billion dollars