Donation Method - Ask a bot for a Spare Key!
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.
New Method - Buy the access to Dota 2 Beta
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.
Old method - Join contests/giveaways
Beta Giveaway Contests (by Dota 2 communities)
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.
Beta Tester Selection (by Valve)
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.
Other sources
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Note: this part of the answer is outdated, but I left it alone for now.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
Yes you can. (This is basically BlaXpirit's approach but without the modification since it is unneeded)
Bindings that are done via a config file will not be shown in the game (the hotkey square is emtpy as if no hotkey was selected) but still apply.
To do this you need to go to your dota folder
dota 2 beta\dota\cfg\
and create a file calledautoexec.cfg
. This file will be automatically loaded on startup from DotA2. (more on what autoexec is here: What is this autoexec.cfg, and what does it do?)Next thing to do is opening config.cfg and copying everything containing
bind
into the autoexec.cfg. After this you need to delete the old ingame bindings by going into the ingame settings menu, leftclicking on a binding and then rightclicking it leaving it empty.The next time you start DotA2 the bindings from autoexec.cfg will be loaded automatically and this will result in blank ingame hotkeys. (I assume this is what you wanted)