I am in the same boat. I got several bad grades my second semester and was academically dismissed. I asked my dean for a 505 letter and as I expected, he said "nope". They won't help me go to another school.
If you had a decent guy or gal as dean at your former school you may have a shot. He/she may help you out. I appealed to his sense of "karma", but as I expected he refused to help me and I knew a 505 letter is not typically given. There is no obligation to do so and don't bet on it.
You will probably have to wait the standard 2 years per ABA rules. Do what I am doing- get a master's in something you enjoy and apply to another school for fall 2012.
In my case I ended up in a lower tier school that dismissed 40% of their 1L class. Now that I know this, I am saddened that I ended up going there. I wish I knew better, but that's life- live and learn. So I am going to take the LSAT again and apply to schools that try to help their classes succeed versus the "weeding out" approach that some law school use to up their bar passage rates.
There are schools that have attrition rates as high as 40% and school with rates as low as 0%. I can not stress this enough- pay attention to attrition rates. I simply did not know some of the inner workings and how different some schools can be. I probably can apply to my former school after 1 year, rather than 2- there were so many people in the 1L and 2L classes there that were on their "second go"- creepy ehe?- should have seen that as red flags after my first week there. Most schools, I believe, allow for this. So if you want to deal with your old school again you may only have to wait 1 year. As for myself, I do not. Do your research and you can end up alright.
I have been researching quite a bit on what students do after academic dismissal. It must happen often. There are maybe 7 or 8 schools, if not more, that have 30% plus academic attrition rates. That's hundreds of student per year. Surprisingly, there is little that I have been able to find. Or maybe it's not so surprising due to the embarrassment involved. I did look at the some writings from the author of Dismissed Law Student Essays available for free on line at lawschoolcrossing.com. They are not very useful to either of us. The author was dismissed and decided not to go back. She mostly writes about her emotional state, not practical tangible information. It is more of a pep talk. Not a how to.
If you find something in your own research, please post it. I will do the same. Good luck.