Disclaimer:
These here mentioned are only personal experiences hence are not guaranteed to be 100% accurate or even true.Update :
As you might have noticed Google killed the supplemental tag. This discussion is still valid but you can no longer directly measure results by using a Google search. Changes will only be noticed in traffic.
Supplemental index is where sites go for bootcamp or penitence. They spend some time in the Supplemental Index facility training / praying and emerge stronger and ready to put up a fight or they never find the way out and remain there as reminiscences of their former selves, neither dead nor alive, simple fat that making Google's index look bigger and helping Google provide more and more results even if most have long succumbed.
There are two answers here actually. First answer is that they done something wrong and go there for penitence. Duplicate content is as wrong as it gets. Compiling a site from pieces of many others will trigger duplicate filters and send your offending page straight to the Supplemental Hell.
Lack of relevant text on page will also get you there. By relevant text I'm not talking about a navigation menu and 3 sentences scattered on the page. Google sees the repetitive content in your site and that is no longer considered relevant. So when you put out some text make sure you have several paragraphs and try to keep repetitive textual site sections to a minimum. If your menus have a lot of text think of making them images with not titles or alt tags. This will no longer give your site a repetitive content and will allow you to create relevant text with fewer actual words. I think for a site to be considered relevant text has to seriously outweight the repetitive slices of the site.
Over-eager beaver seos go down too. If you link spam your way in the serps with no relevant links related to your real content and page theme you are a problem and you need to repent. Do not build too many links too fast. That does not happen in real virtual seo life and in 99% of cases it has not been used a legit way to get those backlinks. The other 1% do not need to read this page ;)
I also believe most rookies hit the Bootcamp. Thousands of pages are launched daily and they have to proove themselves worthy to take the places of the veteran websites or even compete with them regardless of their content. Even if you bring in the new juice experience (almost) always wins. So a new site will hit Supplemental Index unless ... read on.
Do not orphan pages on your site. All pages must be reachable on a deep crawl. Make sure you have a sitemap or somthing unless you have an accurate database driven structure on your site which won't loose pages on the way.
It's as bad as it gets. You virtually get no traffic. Not even long searches pull you out to get a lousy worthless click and, unless you have typos and users search for them, you get no visitors. Only if no Regular Index pages exist for a search you get the charity hit. But usually it ain't worth building sites aiming for searches with no real reputable results. Yes, there is no competition but no interest either from serpchers.
If you only have a few pages inside, they might come out quite soon alone. Just build your main pages and make sure you link them. But if your entire site slips inside you have a problem and in worst case scenario you get hammerd (banned). This usually happens when your entire site is dupe content borrowed from other sites.
It takes work, balls of steel and seo skill. If you got there and no duplicate content is involved and you are not completely banned within a week tops you have a chance.
To get out you need the juice: the links. So others get to pull you out of the Supplemental Results Hell. It's not up to you or is it?
You need backlinks to get Serps Rep and only when you have a Serps Street Reputation you can exit. So you have to build links. I'm not planning to tell you here how to get links but :
Remember to keep links on topic. Do not just get them from anywhere for the sake of count as Google. They won't help much / for long. Too many offtopic links simple stamp Low Life Spammer on your forehead and it's a rough ride removing it. I've been there and I know. And your site will be banned. Sooner or later.
If you plan to spam make sure you get some legit links first and when you get a little Rep go for spamming. But cover your tracks. I might show you how to do this at a later time.
I placed a new link on my site and I'll show you the status of my pages related to search engines and supplemental index. It's a nice experiment as this new White Hat Seo site of mine has some pages used for navigation in the Supplemental Hell. You can help me save them :) Check out the Spider sign just below in the Site Footer. Bookmark it for further use!