This site only gives the calls published in the last two weeks. However, on clicking on the specific programmes above the page (e.g. Ideas for the European Research Council, People for the various Marie Curie actions, etc) you find all open calls.
If you find a call that interests you, click on "Call identifier", and you find links to the (many) documents you need to consult. The first place to go is to "Information package" (click on the + next to it). You need to read all documents there. They are long, but have good tables of contents.
Applications are done through the Electronic Proposal Submission Service (EPSS).
Note also that every country has National Contact Points to help you in the preparation of an application. Usually, universities and research centres are also very helpful.
On the left of the first page, you find links to various kinds of information on the whole Framework Programme.
This page also indicates how to subscribe to the mailing list that informs you of calls in your field of interest.