What's the best way to get sleep on a train in a sitting compartment?

1. Bring a self-inflating camping air mattress such as a Thermarest.
2. Rearrange the luggage on the luggage rack to make sufficient room. 2a. Put some of the bags from the luggage rack on your allocated seat if necessary.
3. Lay your camping mattress on the bars of the luggage rack.
4. Get at least some of the other passengers onside by making light of it (presumably the luggage rack bars will be too uncomfortable for anyone without a camping mattress to consider it)
5. Climb up and go to sleep.

I did this a few years ago in Kenya on a train from Mombasa to Nairobi. A ticket inspector came around about 10 minutes before we arrived and was not impressed ("how can we be having such elements on our trains!") but by that time it was around 7:30 am - time to wake up anyway. It was actually very comfy.

In addition to the preparations suggested in other answers, I'd like to add an upright sleeping technique that works well in my experience. Check this guy out:

It's a surprisingly comfortable position. I've taken multiple-hour naps on several flights this way. It doesn't require sitting next to the window or aisle, and it doesn't require multiple seats.

He's resting this specially-designed pillow on the tray in front of him, but it could be rested on your lap. Pillows like these tend to be collapsible and/or inflatable for travel convenience.

If you don't want to buy a special pillow, you can just use a large backpack or similarly-shaped piece of luggage. This is what I do, and it has the bonus of making the bag you sleep on particularly difficult for pickpockets and thieves to access. Alternately, multiple regular pillows (or one body-length pillow folded up) can do the trick too, especially if wrapped in a blanket or towel to keep them together.

Leaning against the window. Optionally resting on your hand with elbow against the bottom of armchair. Also, crossing your arms, with your hand tucked under your arm pits, can help to keep warm while sleeping enhancing your resting: then lean to the side of train wall to hold your body.

A few more tips, I do long commutes:

Don't rest with your head on the window, so you won't grease it grossly with your hair. Find a place with sufficient train wall with no window. Sitting by the window, is also the best place for charging devices like a phone. While charging, the battery of the phone can keep your hand warm for a while. Use an iPad charger, it charges faster. Being on the window side, there can be AC on the ground of the train window, to warm your feet. Also, bring the daily commute newspaper with you. If no one is in front of you, you can place the the newspaper on the seat and put your feet over it, without having to take off your shoes. I would also prefer now a wider phone, instead of an iPad for videos, either you need to carry both devices all day in the bag.