If you would like to start building Azure machine learning experiments on Micosoft Azure, You will be able to start getting started with Microsoft free offer for Azure feature-sepcific offer where you can work on Azure ML without a need for Azure subscriptions.
All what you need is a Microsoft account to login, once you got that, visit below link to start experimenting Azure ML.
If you don't have a Microsoft account (Live, Hotmail, Outlook), here you can sign up for free:
Update: Due to a recent update in Azure ML site,You will be able to use Azure Studio as a guest and you don't need to login or create a Microsoft account.
We recommend you to create a Microsoft account to store all your experiments under you account to be available everywhere.
Enjoy Azure ML!