Being a foreign worker in the US, this means I actually lost three things - my passport, my I-94 and my US Visa. I fortunately have a I-797A which establishes my employment status, but is not useful for re-entry into the US.
I went to the Australian Consulate in San Francisco to apply for a new passport. I applied on the 28th of May, they deposited my check the next day, and I received my new passport on the 4th of June. Waiting time -- less than a week. Replacement cost -- US$209 (including lost passport penalty fee).
The US documents -- the I-94 and visa -- will be much more difficult to replace.
The I-94 is the little piece of card from the bottom of the form you fill in when you enter the US, which gets torn off and stapled into your passport. It is nothing more than a piece of paper with a number stamped on it. Nowhere near as complex as an e-Passport. To replace it, you file a form I-102, provide as much documentation as you can, and pray. I've sent in the form and a check for the US$320 filing fee -- the check is yet to be cashed, and I haven't had any response. Apparently I shouldn't be surprised; the USCIS have released some information on their form processing time which suggests it should take around 3 months to process the form, and external parties claim a time closer to 6 months.
Of course, the situation for me is nowhere near as bad as it is for many. If this was my first entry into the US for employment purposes, I would be unable to get a social security number, be paid or get a drivers license, for several months (which is also possible through just filing for the social security number too soon after first arrival). However, I cannot leave the US until my I-94 is replaced, and that in turn will hold up replacing my visa. Which brings me to the honeymoon. We had planned to spend our honeymoon at a resort in Cancun, Mexico. Without an I-94 or visa, that is not an option, and I am trying to determine if we can safely visit Puerto Rico (the CBP site repeatedly says that US Citizens do not need a passport to travel to or return directly from Puerto Rico by air, but is completely unclear as to what non-citizens need). If not, we might end up delaying our honeymoon.