Let me tackle the issue of the site's content, in terms of Search Engine Optimization (SEO) first - because I think it's one of the most impactful. I have an additional blog post on how to improve your Drupal site's SEO by improving its site structure to allow it to be as search-engine friendly and easily crawl-able as possible. However, let's not lose sight of the fact that what's ultimately getting crawled, indexed and matched to a site search is your content. If your content isn't good, specific, or very much (quantity-wise), you won't be matching many searches regardless of your site's awesome SEO-friendly structure.
Sooooo, let's talk about how to improve your site's organic search rankings (organic, meaning that this isn't related to Adwords or paid advertisement), from a content point-of-view.
1. Quality content
Again - your site's content is ultimately what's being crawled and what'll be matched up against search terms. If your pages don't have very much content (I've even seen sites where the majority of the content is embedded in images, i.e. not crawlable), or simply do not contain the types of words, phrases or questions you think folks may be searching with, there won't be many search matches. That's that. Content is king when it comes to SEO.
My main advice for this section is not to go crazy in trying to force search terms & keywords into your paragraphs unnaturally. Simply write good quality, longer (more than a few sentences) content on your website to get higher rankings. If your content is good, specific, and useful, users will end up finding it, spending more time on your pages before bouncing, and your rankings will improve naturally over a longer period of time. Going down the rabbit hole of figuring out the best targeted keywords and then trying to force them into your content when you wouldn't normally use them can be weird/fake if you overdo it. Plus, chasing an immediate pay-off, rather than long-term popularity is always an iffy goal. So I typically advocate for having natural, good quality content of a certain volume (a single paragraph in a page may not be enough to appear very close to the top of a search) to check this requirement off!
2. Links to your page from external sites
Now if you're already completed #1 and have content on your site that's relevant to a certain search, how do you increase the order in which your page appears on Google's search results page? You want to move closer to the top, after all! Well... that's party due to the specificity of the match, but also partly due to your site's reputation!
The most important thing you can do to improve your site's reputation is to have external sites link to you! That, of course, includes social media mentions. So, get folks tweeting about your content, and get your site's pages mentioned and linked to on other websites.
Think about it this way: How is Google, or another search engine, going to know which of all the websites that sell running shoes is the most respected and trusted? How does Google figure out that you'd want to see the 'Nike' site toward the top, as opposed to the knock-off site from China? Mentions from peer sites, of course! Google's not going to come asking you whether you're the most trusted in your field, but it's going to trust what your peers say! So if others are linking to you profusely, your reputation is really going to increase.
Additionally, a link coming from a very reputable site, like cnn.com, to yours would definitely be worth multiple links from never-heard-of blogs, so it matters who does the linking. But all incoming links are valuable and a variety of mentions from websites and social media will definitely help your case!
So go spread the word about your site!
3. Content freshness
Finally, and this is definitely not as big of a deal as the two issues above, but content freshness has a small part to play in the order of results too. How often do you see search results include posts from 2006 anymore? Hopefully not too often, unless the number of results is so small and the post you're picking up is super-specific to your search keywords... Google definitely wants to serve you the latest and most up-to-date info on whatever topic we're searching for, so there's a favoring towards more recent content. So just make sure you keep your content nice and fresh!
Good luck with increasing your rankings! Comment below if you have other tips as well.