I can absolutely relate to where you are right now. You'r likely in a position where the expectations are high and the resources available to you are low. Now the question is, can you generate website traffic with $0 marketing budget. I would like to emphasize I am asking can I and not how can I because you do need to consider if this can actually be done before you make unrealistic promises you cannot live up to.
There are a few ways to go about this and as you do, keep track along the way to mark your progress. And remember, use incognito windows to see search results that are not based on your history of web activity.
1. SEO or Search Engine Optimization
Is your website optimized? Take a look at page titles, descriptions and keywords. Make sure they are related to the page content and are unique for each page. Also incorporate sitelinks linking keywords on your pages to other related pages on your site.
Content doesn't mean you have to setup a blog and start writing. It could be as simple as breaking your web pages into more niche topics, adding an FAQ page and considering non-searchable content such as PDFs and how you can convert some portion or all to on-page content.
Other sites that link to yours will help drive credibility for you site. But don't engage with a company that will promise 100s of backlinks because that will be flagged by Google as spammy. Participate in online forums, answer questions on related blogs, ask partners and affiliates to link to you. If you have budget for any PR, syndicating through a site like PRWeb can also help.
4. Organic Social Media
Do you have a Facebook page, LinkedIn profile, Twitter account, etc for your business? Start sharing content, tips, fun videos and other engaging content and link back to your website. But remember, don't use this as a sales channel!
5. Placement Everywhere
Make sure your website is in your email signature, on your LinkedIn profile, print materials, etc.
I hope this helps!