Most of my flights into LA have arrived late morning/early afternoon. Normally, an early night (maybe even as early as 4pm or 5pm) is all it takes, and I am/we are ready to go the next morning. We might be a little tired but nothing major.
On our last trip we flew from Brisbane to New York in one hit. I think we dozed on the LA-NY flight (kids slept), arriving at about 8pm. We went straight to bed when we got to the hotel and were ready to hit the sites the next morning.
Coming home can be a bit different. I think all my direct flights from LA have arrived into Brisbane around breakfast time. I'm usually asleep at home by about lunchtime and sleep until the next morning. It might take a day or two to get back into a normal sleeping pattern but that could also be due to not having anything exciting (eg
Disneyland!) to get up for the day after the flight.
Generally, I just follow what my body tells me - there's no way to fight it if it's demanding sleep. Oddly, I found flights from the US to UK/Europe take a bigger toll even though the flights are shorter. If I arrive in London at 6am and my body is demanding sleep by 10am, then that's what I do.
But overall, it just takes a night's sleep and things are fine the next morning.
I have to confess the first time I flew from Auckland to LA (at age 20) was a real shock to my system. I'd regularly flown between Australia and NZ, but onto LA was a different thing altogether.