I noticed that there is a surprising lack of Documentation on the System>Settings>Redirection Rules page of the admin panel and even more surprisingly very little about it on the Community. So here is a little bit of info for any admin no matter how much experience you have. It should be said that I am not an expert on redirects but wanted to share what knowledge I had since i was having a hard time finding details.
Order of Redirection
While it should be fairly self explanatory the redirection rules process from top to bottom. If you have 2 redirection rules that cover the same page the first of them will be the executed rule.
Types of Redirections
While the menu shows both 301 and 302 rule types it does little to explain them. The types mean little to the end user but a lot when it comes to search engines. 301 redirects, also known as permanent redirects, will let a search engine know that they shouldn't keep the old page but instead crawl the new page and return that one in search results. 302 redirects, also known as temporary redirects, are rarely used. 302 redirects tell the search engines that the move is only temporary which will cause some search engines to continue to index the old URL, and disregard the new one as a duplicate.
Simple redirections are just that... Simple. The Input can be either Http://www.yourcommunity.com/redirectedfilestructure/ or /redirectedfilestructure. The same goes for the Output URL.
Regular Expression Redirections
These are a bit more complex but are very useful when moving a Space. When moving a space you likely want people to be able to find the new location no matter what section the user may bookmarked or linked to.
Try Input URL: ^/community/OldSpace/(.*) OutputURL: /community/NewSpace/$1
This will redirect everything within the old space to the same file structure within the new space
For going from a group to a space use
Try Input URL: ^/groups/OldGroup/(.*) OutputURL: /community/NewSpace/$1