Here's how I would tackle this.

1) Make sure your "offer" is kickass and provides overwhelming value to your prospective customers. I would focus on a long-form content (PDF, ebook, slides) or actually something free that people would otherwise have to pay for it.

Takeaway: you gotta give people a really good reason to sign up for something.

2) Create a landing page that drives conversion. Ideally your whole web presence should be strong but specially your landing page for this "online offer" needs to be flawless. Design for trust. For example, be specific about what the person will get for signing up using normal language. Don't say "sign up for this valuable ebook" instead say "Learn how to XYZ with this 32-page practical ebook."

Unless you're really well-versed in web design, you'll want to probably have someone help you out here. I'm happy to give you advice. There are also some services out there like http://unbounce.com/ that will help you build good landing pages.

Don't forget to track everything you're doing so you can run some experiments like A/B tests.

3) Driving the traffic. It boils down to either inbound or outbound. Long-term you're better off with inbound-heavy approach. That mean content, content and more content. Again, you might need someone to give you some initial pointers here. One of the approaches I take is to tap into freelancer networks like Upwork.com and others to help me create content quickly.

As far as outbound, I have a little Linkedin hack I use with Linkedin groups. But in short it all depends on your industry and what you're trying to sell. Facebook ads is very easy to do it yourself and start with very small budgets. Growth hacking here is key. Even if it mean you reach out to people one by one on Linkedin, sometimes you just have to hack your way to momentum.

4) Optimize and test like crazy. There are a lot of tools here to help you like Optimizely (too expensive) and likes https://www.quora.com/A-B-Testing-What-are-the-alternatives-to-Optimizely

Honestly, it will all come down to short term vs longer term approach here. It's hard to give you more advice without more context around your product, company, industry, etc.

I'm happy to chat more. I'm brand new here but love the idea of helping others solve challenges. I'm currently managing a multi-million dollar program with hundreds of freelancers and 10 employees for a Fortune 50 company.

Thanks!