How to expose the node creation form in the front page? I created a new content type "project" and I want to create a view where every one can add a node (create a content) with my content type.

How to expose the form (to add a new project node) in the front (I do not just want to expose a link to add such node)?

In admin/people/permissions I granted the permission for ANONYMOUS USER to be able to create a new content.
To display content type form you can use formblock module as it description explains:


  Enables the presentation of user registration, site wide contact, or node creation forms in blocks. This is particularly useful for including forms on panels.



Enable the module
Go to Project admin/structure/types/manage/project
On the bottom left vertical tabs there'd be a Form Block, check Enable data entry from a block and save
Go to admin/structure/block and enable Project form block




I hope this'd help you.