Some of this does depend on time. There's a lot you can do now that you couldn't in 1996.
UPS keeps sender info on the package itself. They won't take a package without it. I think the same goes for most other package delivery companies. Nowadays, you can even log into UPS's website to track your packages as they go from state to state.
The closest you can get to anonymous is to drop a letter in a mailbox on the street (the blue things found here and there, mostly near post offices, libraries, and other gov't buildings, but sometimes on seemingly random streets. I believe their UK counterparts are red pillars).
When it gets picked up, it'll be brought to the nearest post office. Assuming it has proper postage and everything, they'll stamp it with a postmark. That tells you the day it was stamped and the post office that stamped it.
From that point, it simply gets sorted and sent. Any other info will come from you. If you don't mark a return address and are careful to wear gloves (even though fingerprints will probably be smudged during sorting, handling, and delivery), the recipient will never know anything more than the day and town where it was collected.
That assumes, however, that you're just sending a letter. I'm not sure of the exact restrictions, but at a certain point, a large bulky envelope becomes a package, and that must be sent by package delivery (FedEx is an extension of the post office, but UPS or DHL or another service is perfectly acceptable).
Hope this helps.
Paul
