In this SSRS Tutorial I will show you how to give users access to Report Builder 3.0 using SSRS 2008 R2.
I will give you short answer to this question and at the end I will provide link to Microsoft site explains that in details.
1) Go to Reporting Services Server Properties. You can do that by connecting to Reporting Services instance (not database engine) in Object Explorer (SSMS) right clicking reporting services instance and clicking Properties
2) Go to Advanced Section
3) Set EnableReportDesignClientDownload to True. (Sort the list in alphabetic order if you cannot find the property)
4) Microsoft documentation doesn't mention reporting services "restart" so it might work without it.
5) In Report Manager give user "Report Builder" role on the folders you want the user to access
6) The final step which is a bit of suprise to me; you need to give user System User access. To do that go to Report manager and click site settings link (top right corner) if you cannot see it you most likely don't have permissions necessary to make system changes. Add user and give the user System User access
Below is link to full explanation with details.
How to: Configure Report Builder Access
I hope that helps you to see SSRS Report Builder 3.0 permission so users can access and use the tool.