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

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.

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.

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.

Get a Window Seat

When I reserve a seat on train (or a plane, for that matter), knowing that I would like to sleep during the journey, I often book a window seat. That way I can lean my head on the window, rather than having it hanging in the void, causing me to wake up every ten minutes as soon as the neck ache kicks in. Moreover I place a jumper/t-shirt/soft-layer between my head and the window. This layer acts as a pillow and temperature insulator.

As the comments below suggest, the windows seat is also strategically placed so that you will not be woken up when your neighbour needs to go to the bathroom. However, you can always climb on top of the seat, or find another acrobatic way out, in case you are the one who needs to go to the bathroom. From my point of view it is better to be the one climbing over rather than to be climbed over.

Pack for Sleeping

If you want to sleep, bring sleeping gear. Since you are travelling by train, you don’t have to abide by weight rules for your carry-on. So you can pack as much gear as you like. For me, necessary can’t-sleep-without-it gear includes:

• Sleeping mask
• Ear plugs
• Travel pillow
• Some form of cover: blanket, jacket, sleeping bag

Anticipate Pickpockets

As others have mentioned in the comments: sleeping on a long-haul night train makes you a target for pickpockets/thieves, especially if you don’t have the extra safety of being inside a private/locked compartment. To be fair there is not much you can do to make yourself, and your stuff, completely 100% thieve-proof. More so if you are sleeping in an unlocked, unsupervised space. What you can do however is make sound assumptions on thieve behaviour and plan ahead. Your objective should be to make your stuff less appealing for thieves because it requires more effort on their part to take it.

Here and here are some general pickpocket-prenvention tips. Here is some advice on sleeping in couchettes on Italian trains. Below is a summary of what I think are the most relevant points for the purpose of sleeping in a train:

1. Keep your money/documents/phone/valuables on you, either in your pockets or in dedicated supports (for example money belts). Clothes and other less-valuable items can go in your rucksack/suitcase.

2. If you have a small backpack/laptop bag, strap/clip/tie it to some fixed support. This can be either your leg, the seat itself, the table between seats, etc. The point is that anchoring the bag to a fixed support makes it harder to be snatched away.

3. Similarly, you can also strap/clip/tie your rucksack/suitcase to, for example, the luggage rack. Once again this makes it harder to snatch.

4. Lock the zippers on all your bags with padlocks/zip-ties/key-ring/paper-clips. This will obviously make the bag harder to get into.

5. Make sure that the topmost item in your backpack/rucksack/suitcase is something that a thief would have no interest in taking. My personal favourite are dirty underwear and socks, kept in a plastic bag with its opening towards the opening of the backpack. This way its content is the fist thing a potential thief would see, when accessing the bag. I always laugh when picturing what their face would look like.

Final Remarks

Having said this, note that I somewhat agree with this guy:

If you’re determined to avoid paying for a couchette, [and fail to find anything else but a standard (non-foldout) seat] book a couchette — what you’ll spend is less than what you’d waste by arriving at your next destination too fatigued to enjoy it.

This is especially true in case of long-haul train journeys such as the one you mention. Moreover, couchette compartments can be locked from the inside adding an extra level of safety for you and your belongings.