dota-2
I know programming and am aware of the Dota 2 API. However, after searching about I couldn't find out whether the information about the region / server of the match / replay is stored somewhere.
This is necessary as I plan to analyze replays based on which regions they are from.
There is a Steam Community bot that people donate extra DotA 2 keys to. You can add the bot as a friend and send him the private message "give dota" to get a DotA 2 key sent to you. You can donate any extra keys you end up with afterwards.
Valve gives now the possibility to buy directly an early access bundle through Dota 2 Store. The bundle contains the beta access key and some collectibles.
One legal and legit way, is to participate to one of many contests available and hope to win. The official community of Dota 2 is PlayDota. I suggest you to register to to that site, because since the launch of Dota 2 Beta it was the main beta key distributor, through random beta keys giveaway (hundreds if not thousands key already distributed).
There are many other places around to check and it has no much sense list all sites here. Just check PlayDota forum and Dota 2 Reddit Channel, that are the two main Dota 2 international community sites at the moment. If a new giveway starts, it is usually advertised there.
SteamGifts is also an interesting community driven gift website (that support Steam logon) that often has Dota 2 keys.
If you don't have time, skill or attitude for a contest, you can try to install Steam and fill this survey.
It is an hardware survey followed by a simple questionnaire that will be used by Valve to target potential beta testers. Identified subjects will receive the beta access and 2 additional keys to invite some friends.
Be aware of scammers sites or people that try to sell you fake keys, there are many around. Also buying valid keys infringe Steam rules, so just avoid it.
Update as of 18/1/2013
The options menu has been changed to make it easier to find the control rebinding for items. I have taken a new screenshot - simply click on steps 1 through 4 from anywhere in the game client to open up the menu and rebind your item hotkeys.
Note: this part of the answer is outdated, but I left it alone for now. If it's appropriate to delete it, mods are welcome to do so.
You can change the key bindings for both abilities and items by clicking their icons underneath the list of controls in the options menu. Below is a screenshot of the controls menu, you can see that I reassigned my items to numbers 1-4 and my extra mouse buttons.
It is not immediately apparent that these buttons which look like the ingame HUD are actually additional key binding options, but each one that is labelled can be changed.
It's also highly recommended that you rebind at least a few control group keys to something else, but it's rare that you will need all 6 control groups in a normal game. I chose F1-F3, but you can use whatever you like.
Best Answer
There is a way to know the Server if you know the replay id of the game. If you have obtained the replay id match, you can paste it here http://www.dotabuff.com/. After that, the overview of the match will be reflected and the server is found on the top part fourth column.