Great question. We wrote a blog post about this very topic but I would be happy to summarise a couple of the main points for you:
Keywords - this is about understanding what your target audience is likely to be searching for in Google. In your case, it might be something along the lines of ‘tutoring centres in New York’, or ‘private tuition for high school’. If you have these keywords show up in the main areas on the relevant pages on your website, you can attract the right kind of traffic to the right place.
Get Online - it is super important to have a good online presence both in terms of social media and content creation. Being active on social media channels allows you to engage with your users whilst also improving your SEO. Additionally, writing your own blog gives you quality keyword content and a high index of pages, all of which helps you build up your SEO.
Furthermore, you can look at optimising your page content and getting your company listed in online directories/on other sites. Using built in analytics on your social media accounts and setting up Google Analytics on your website will also help you track your SEO performance in order to refine your content.
The main thing to stress is that good SEO takes time to build up and so being as proactive as possible, in creation and analysis, will stand you in good stead.
I hope that is useful information, Sarah!