It's rather doubtful for a single page to rank high, however, it all depends on what the content of the website is about, what market does it target etc. For example, if you have a lot of friends on facebook, followers on twitter and other social media and you have something cool you want to show, you can try and draw the traffic through social media. But in reality, high ranking websites are the one with a lot good quality, frequently updated content. The other solution would be to have A VERY LONG one page website...;-) Good Luck! Share your results;-)
It kind of depends what key phrase you want to rank for. If your single page has a lot of good content, well optimised titles etc etc AND plenty of backlinks then yes, there's no reason why it can't rank high. However, since search engines take every bit of readable text on a website into account - including the size of a website as a whole then if the subject\key phrase that you want your site to rank well is competitive then it will be hard.
Every now and then a pearl of wisdom about SEO pops up at DP. As a rule, this is not the best place to learn or get advise about SEO. Everything that has been said about SEO here, has been said better elsewhere. Throw in the perpetuated myth-mongers and one-line spammers, and you get nothing but noise. If this is a single page wonder site, you are going to have a tough time getting it to rank. If you expect to be making money from this page, then you will have to spend some money via AdWords (or similar programs) and maybe some unethical link brokering.