This is also called "Split Martingale" or "Cross-Out" or "Cancellation" or several other names.
In its simplest form, you write down some numbers... let's say 1 2 3. Each bet is the first and last of these numbers. In this example, it is 1 and 3, which equals 4. If you win you cross off the number two and bet the next two that are on the outside. In this instance there would be only the single two-unit bet. If that wins you complete the series and win a total of all of the numbers (six here). If the bet loses, then you add that one number to the end of the series. So, the first bet would be 4 and it loses, so you add 4. That makes the next bet 1 plus 4, which are 5. And so on....
This means that you need to win only 1/3 of the bets PLUS two more and you will complete the series and win the amount that is in the series. Since you normally will win ALMOST half of your bets, that means that you MUST win... or must you?? The mathematicians will tell you that this is another method that will eventually reach the point where you either run out of money or surpass the casino limit for bets.
I have also seen this done with many variations. One would be to use different numbers, such as lots of ones in the beginning, to keep the series from growing so fast. So, the series would be something like 1 1 1 2 2 3. When you complete the series you will win 10 units. The first bet is still four. You must win 1/3 plus 3. You may also want to try a series like $10 $10 $20 $10, which will win $50 when the series is completed.
Other people have devised ways of splitting it up when the bet gets too high. Set it aside and win one series and then go back and finish the second series. This would require a higher percentage of winning decisions.
There is a "Reverse LaBouchere" for the brave at heart. You add the amount of the win to the end, and cancel the 2 outside numbers each time that you lose. The bet is the sum of the two outside numbers. This gives you many very small losses in return for an occasional very large win. You would have to set a goal in some way, such as when you hit the table limit and let it ride until it loses. That would be the end of the series. Each time that it loses, you will only lose the amount of the numbers that you put down in the beginning of the series.
It is wise to have some kind of money management with any form of the LaBouchere strategy (as it is with all strategies in general). You may wish to play the 10 10 20 10 series with a maximum bankroll of $500. You would put away all winnings never to be lost again on this strategy. In that way, once you complete 10 of these series you have the required bankroll and will not lose any more. Stop when you lose a $500 bankroll (whether it is your starting bankroll or winnings). This is one suggestion. You can devise your own.