You won't be able to rank a single page perfectly because you are at a severe disadvantage. However that shouldn't stop you from being able to rank well. First to understand why you wont rank perfectly: Google and Bing both prefer quality content and lots of it. A single page website generally cannot provide fresh and new quality content to keep search engine crawlers visiting your website frequently.
However I assume that you are really wanting to keep your single page website and dont want to waste the time or money you've spent creating it or having it created. So your best option is to create some really great relevant web 2.0 articles, do some social bookmarking, get some amazing relevant followed inbound links, make sure your keywords are in place and working (focus each section of the page on a grouping of keywords which are all related to each other - watch out for keyword density) and constantly work on boosting social media signals. You may also want to consider developing landing pages which funnel your visitors to your main page and which can also help boost your ranking for your keywords - these landing pages will also help get you crawled more frequently especially if you are building some really good inboundlinks. Beyond that if your website is semantically correct and you are meeting every single SE best practice you should atleast have a fighting chance.
A single page website/blogpage lacks one thing that Google looks for - quality content. Quality content should be unique, precise and fresh which means you need to have a blogpage that is updated as much as you possibly can.
Even if your website has only 1 page you still can rank well in SE (as long as your niche is not competitive). In general you have to ask yourself the question:"Is my site better than my competitors?"If answer is no, why the search engines should rank it for? Add value for the users and you will get rankings as well. For exmaple if you have a cleaning agency in Chicago, you can add cleaning price calculator on your website. This will be sign to SE that your site has something valuable for the users. Apart from great website you will need to make on-page SEO - optmize your urls,make your page titles and meta descriptions unique and descriptive, add alt tags to the images,remove duplicate content and add canonical elements to the pages. You also need to do some off page seo - create social media pages for you website/business and engage with users. Get some quality backlinks from authority review sites(like Yelp) and ask your clients/users to leave reviews about your services. SEO is not one day process - you need to spend some time and money to get good results in long term.
@Sathyakumar23 you are correct on page is also important I would say that almost all the member over here is talking everything over to one direction i.e. the off page because there's nothing to that much extent you need bother with the on page thing but you are correct it do carries weight !