When configuring the site, you can choose to display, hide, and position blocks on the site's front page. When configuring a course, you can also show/hide/position blocks on the course's home page. The procedure is the same whether working on the site's front page or a course's home page. The site's front page is essentially a course. You can also give students permission to add blocks to their personal My home page and to their My profile page.
Many blocks are available to you in a standard Moodle installation. You can also install additional blocks, available through http://moodle.org/plugins.
