All this data is potentially out of date, and should be taken with a truckload of salt
Lotteries are player-run lotteries within the EvE universe. They offer a low level of entry (all the way down to 1 million ISK per ticket) to anyone who wants to win great prizes.
In order to participate in a lottery, you should direct yourself to the Sell Orders forum found here. After you find one, you should completely read the instructions on the first post.
Lotteries will usually run from 1 week up to 1 month and prizes are usually handed out through the contracting system.
Like anything in EvE, security can be questionable at times. For this reason, you should always look for lotteries with known third parties on board (Chribba, Grendell, Darknesss, etc). Although these three have handled the most ISK, there are a few lesser-known third parties who also host lotteries. There are also other well known people that host lotteries without a third party (T'Amber). Check references for any third party to ensure they can be trusted-- in Eve, anyone can pretend to be whatever they want!
In order to draw numbers you must use a system that is user-vetted and widely approved. For this reason, you should always look for lotteries using Chribba's Dice. This site is free to use and is tied to your API key to ensure security for lottery players.
Lotteries will often use ticket tracking systems to monitor who has bought tickets. These systems link to a user's account using a full API key. CCP allows trackers to be updated once per hour via a data pull from the user's Wallet Journal. People who host trackers often charge a fee, so some smaller lotteries may also use what is called a forum ticket list. It is simply a list of the ticket numbers that is updated as they are bought.
Entering a lottery the right way
The standard idea is that you send the amount of ISK for the tickets you want to either the person hosting the lottery or the third party, including a reason code specified by the lottery rules (to allow for ticket tracking).
The best idea is to copy the person's name into the People & Places section of Character search and just find them. After that, you right click, go to Give Money and then enter the amount (amount of tickets you want times the cost of 1 ticket) and include the reason code. Due to problems with fonts in EvE, some characters look very similar (0 & O and B & 8), for this reason, you should also copy the reason code directly from the thread.
Running your own lotteries
Lotteries are not a magic get-rich-quick scheme. Try starting out with a small lottery just so you can see some of the problems that can arise.
Don't just think that getting a third party and a few prizes will sell a lottery; even lotteries with billions of ISK have failed due to not enough interest by buyers. The key is an engaging format, good customer service, and lots of advertising.
If you're really interested in running a lottery by yourself, there is a guide written by Grendell right here.
Tips for success
Treat your customers well - Don't include phrases in your lottery like "ISK sent with the wrong reason code is a donation" or "Prizes may be added or removed at any time". If your customers do not trust you with their ISK, they will not play your lottery.
Keep profit margins reasonable - It's fine to include your costs for advertising, ticket tracking, etc. in your profit calculations. However, consider that you are competing with many other lotteries out there. 2000M of tickets for a 700M Thanatos will not sell very fast; people will play the lottery with only 900M of tickets for the same prize. Usually anything under 25% is considered a good margin for a lottery. Note that this should include your lottery costs; that is, your actual profit will be less than 25%. Anything above this margin will usually not sell well or be considered a 'scam' by your customers-- or, at the minimum, be out-competed by other lotteries with better odds.
Be active and work hard - You cannot just set up a lottery, walk away, and come back to a pile of ISK. Lotteries take care and nurturing or they will founder unsold. Advertise in local channels (not just Jita local!), talk to your corp or alliance, and keep your forum thread up-to-date.