The table tells you when to take your Melatonin each day, according to how many timezones you are crossing and which direction (East to West or West to East). The dose size is 500 µg (half a milligram).
|timezones|| day before and
day of travel
| first day at
|>=10 E to W||On awakening||same time as previous day||1-2 hrs later than previous day||morning only|
|7-9 E to W||On awakening||On awakening||1-2 hrs later than previous day||midday, not afternoon|
|1-6 E to W||On awakening||On awakening||1-2 hrs later than previous day||late afternoon|
|1-6 W to E||3pm||same time as previous day||1-2 hrs earlier than previous day||morning|
|7-9 W to E||3pm||same time as previous day||1-2 hrs earlier than previous day||midday, not morning|
|>=10 W to E||On awakening||same time as previous day||1-2 hrs earlier than previous day||morning only|
When the table says "same time as previous day" it means exactly 24 hours later. So if I took my melatonin at 3pm in LA yesterday, and I am now in NY and want to take it "at the same time" then I take it at 6pm NY time.
"Getting daylight" means exposing yourself to as much natural light as possible: sitting by a large window, taking a walk outside, etc. This is just as important as taking the melatonin.
When travelling from West to East, you often arrive in the morning, and then have the problem of trying to stay awake the whole day. Getting lots of daylight will help, but if it becomes impossible to stay awake, take a brief nap for 1-2 hours at MOST (get someone to wake you up if necessary). Then you should be able to stay awake until a reasonable local time like 10pm.