How can I generate website traffic with $0 marketing budget?

SEO and Email marketing should work for you.

Use traffic exchange and mailers.

You can generate website traffic to your website by just following simple methods
Firstly, check webmaster tool and find high clicks keywords. Start to boost their ranking to increase organic traffic.
Secondly, As per your website authority, you can work on long tail keywords to increase organic traffic.

Good Content, Social Media and Traffic Exchanges.

Yes, one can generate traffic by SEO techniques, by making as much as backlinks.

guest post ,forum comments,post good article on website,share on social network

Search engine optimization

Social Marketing mostly setting up a proper Fan Page, Blogging, Forum Post like Warrior, Apsense, IBO etc. and mostly SEO if you are a website owner.
Hope this will meet your target.

Social Sharing And MAking Quality backling

Post and Share on groups on Social Media Sites.

Through Social Media and Posting Article

post aricle and get more traffic of your website

only blog posting best way to generate more Traffic.

Only social media is one of the best way to generate more Traffic.

Doing off page SEO and Share content & Images on Social Media - these both through generate more traffics Off Page SEO activites likes:
free and high quality Directory, local submission, Business profile Submissions..
Also doing Create Content and post on Blog and share it on social media
Blog Comments/Forum Posting
Question/Answer
Guest Posting
PPT Create and Document Sharing
Infographic Create and share it..
These are main activities through generate more traffic with $0 budget..

By Free PR and Article, Guest Posting, Social Media, Document Sharing, Image Submissions and Classified Posting

By create more backlinks of your website

Post and Share on groups on Social Media Sites.

share and post on social media sites

guest post ,forum comments on article news sites ,