1) Click on the 'Research' label in the top middle of your Home page
2) On the menu that drops down, click on 'Projects'
3) Use the 'Search Project' block in the middle of the top part of the page, to check that there isn't already a project on your subject. (If there is - go and ask to collaborate on that one, rather than start a new one. Participating in collaborative research teams creates better projects, with more sustained interest & spread of work load, These benefits far outweigh the minor adjustments required to accommodate everyone's visions for the project.)
4.) If there are no other projects on your subject, Click on the green 'Start a New Project' block - and voila! a new project page will open for you - From here, the next steps are pretty much apparent.
Geni's Description & FAQ on Projects: http://wiki.geni.com/index.php/Projects
Starter Kit for How to Add text to a Project: http://www.geni.com/discussions/104799
Starter Kit for How to Add a photo to a Project: http://www.geni.com/discussions/106309
Template Project to play around with: http://www.geni.com/projects/Template-for-a-Project-About-A-Family-...
A more advanced Template: http://www.geni.com/projects/Project-Template/175
Geni's illustrated 'How to Create a Project': http://help.geni.com/entries/21834028-How-do-I-create-a-Project-
A more detailed Step by Step How To - with illustrations - by Curators Pam K, Malka, Erica & Adam: http://www.geni.com/projects/Working-with-projects-Step-by-Step/18185