How, exactly, does the ESTA system work - specifically on arrival?

The ESTA system is pretty much all done electronically - you apply at least 72 hours before you depart, then simply arrive. Obviously you need to present the passport you used to apply for the ESTA waiver.

However there are a few things I think it's good to be aware of, insomuch as they applied to me when I travelled earlier this year - the situation may have changed by the time you read this:

1. If you apply for an ESTA for transit, then within the ESTA validity period you wish to visit the US, then you'll need to reapply for the ESTA waiver and pay the fee again. Sadly, although you can change a few details of a current ESTA, you can't change the type. If you find yourself transiting on the way back less than 3 days following a visit, then I'm not sure what you do! Perhaps the answer is to always apply for visit, just in case.

2. When you arrive, there's probably a queue with a sign that says something like "queue here if you've got an ESTA and have visited the US in the last two years" plus a few other conditions. This is an accelerated border process for people who have already been through the ESTA arrival process at least once, recently. However, be aware that this isn't the whole story - don't do what I did and stand in that queue for thirty minutes only to find out that you need to have visited within the last two years on the same passport - and that doesn't include renewals! Almost missed my connecting flight.

3. It's always a good idea to carry hard-copy facsimiles of all travel documentation. You may never need it, but it seems sensible to me to carry them.

The ESTA program is pretty good though - sometime prior to this travellers to the US from my country had to travel all the way to the one and only US Embassy in the country to get permission to visit, which in some cases might take an entire day of domestic travel and was a significant nuisance.