The main idea is that every time someone links to your website, it is a vote for your website and it will slowly affect your Google rank. However, the worth of each particular link-vote depends on the website that is linking to you.
Websites with a high PageRank of their own (eg ones on the first page of a popular keyword search on Google) will typically help increase your PageRank dramatically when they link to you. On the other hand, websites that are not very popular will not have links that are worth very much.
Also, you get higher Page Rank if the links that point to your website are relevant to its content. If the links are irrelevant, they are not worth as much and so your PageRank is less. Another factor would be the amount of links on the page that links to your website. Getting a link on a website with a high page rank is not always useful if there are a thousand other links on the same page and they are all unrelated.
The only other main factor that Google analyzes when deciding your search engine position would be the age of your website and the websites that link to you. However, that is not something you can usually control unless you buy an old domain second-hand. Is there a way to check your Google PageRank right now?
So the way to make this higher is to gain more good-quality, high-relevance, incoming links?
That must be it. That is all there is to getting a better Google rank, to improving your website's popularity and to making money online. Of course, you may not know it but there are plenty of ways that you can increase your number of incoming links fairly quickly.
For a low fee they will optimize your website for search engines or increase your incoming links through the use of relevant directory websites and SEO articles.