Dota Trade login procedure uses OpenID standard. You can read more about OpenID here: http://en.wikipedia.org/wiki/OpenID
The nutshell is:
YOU ENTER YOUR ACCOUNT'S LOGIN AND PASSWORD AT OFFICIAL STEAMCOMMUNITY.COM, NOT AT DOTA-TRADE.COM
Steam never provides private account data such as password or even login from your account to third party sites (like our, Dota Trade). One thing it only provides when you login - your Steam ID. Yes, WE ARE RECEIVING ONLY YOUR STEAM ID and there are no possible ways of stealing your private account data (even if a need arises...)
The structure below shows the login mechanism.