Stay awake, if possible, as long as you can if traveling East (+ hours). If you are too tired and can take a short nap (half to an hour), do it - just make sure you don't sleep longer than that. Roll around in bed until sunrise if you go the opposite direction. If all fails, take half a sleeping pill at appropriate time, but don't take it more than two nights in a row.

I was an international commercial airline pilot for 35 years.
You don't deal with jet lag .. you just get used to being tired
and trying to make do when you get to your destination.
If you will be there for a long period of time the trick is to get
onto local time as rapidly as possible. Go to bed when local time
says to, awake or asleep - stay in bed or get up at the normal rising time.
Get exercise during the day .... eat appropriate meals when the time calls for it
and don't try to "make things work" by using alcohol or pills.
They just end up screwing with your system.
Best advice ... it takes one full day for every hour of time difference to get onto local time.
Understand this and don't sweat the small stuff. You'll be tired for awhile but once you get
into the local timezone, life gets really interesting and enjoyable.

To me I just sit back for a couple hours then I take a sight seeing tour, and then go back to hotel and take a nap. Your body is tire of the sitting so you have to force your body to move to get energy back in it.Or a spa or a shower should perk you back up.

For me I don't wear a watch. As long as I see it's day light my body assumes its time to be awake.

I always set my watch to local time at my destination when flying and then follow the appropriate sleep/awake pattern. I drink lots of water during the flight and exercise as much as I can......even rotating ankles is better than nothing! This is to keep my body supple.......on long haul it is easy to stiffen up and that makes you more tired.......On arrival - a long shower, pop into the gym if available for a short toning work out - then get on with the remainder of the day!If bed time -I skip the gym but do stretching exercise, then shower then sleep. If available a massage works wonders.