Hi,
I'd first look at why you want to increase traffic, and make sure your plan links in to your final goals- whether it be to gain sales, leads, help customers find answers to questions, engage users, or display advertising content. I'd also ask how quickly you'd like to get traffic. This usually sways the methodology I'll use, so it's always important for me to understand this.
If you're after traffic very quickly, I'd recommend a Google Adwords campaign, which is a great conversion-driven way to generate traffic, right away. SEO will take a bit more time to generate this traffic. In an ideal world, a combination of both can work together for great ROIs.
With a completely fresh customer, I'll make sure Google Analytics and Webmaster Tools are set up and correctly configured, especially for goals and conversions, and E-Commerce tracking if appropriate. I'd also check for major technical issues with crawlability and indexation, there's a great Technical SEO Audit Checklist which you can use from Geoff Kenyon.
From there, there is such a wide range of tasks you can complete to increase traffic, on the SEO side, and I'd really recommend reading Moz' beginner guide to SEO from start to end, to create your plan.
I hope this helps- you're right, it's a very broad question. Moz' knowledgebase has a massive amount of information which you can use to create your plan, I'd definitely recommend you spend time reading through this!
Hope this helps,
Zoe