There are two ways how Google+ can improve your website's exposure in the search results.
First, if you have a massive following on Google+, your Google+ posts, if they are relevant, will appear in the searches that your followers conduct. This will indirectly generate traffic to your website if there is a link embedded in the Google+ post.
On the other hand, apart from slowly incorporating the number of +1s that your website content is getting as part of their ranking signals, they are also embedding +1 info into the results itself (x people shared this on Google+.). Both of these will help boost the number of click throughs from the search result page.
The rules of the game hasn't changed much. It is still about creating quality and useful content that is worth sharing. On the social media (Google+) front, it will be about building and maintaining an engaging community. A business that does content creation and community building best will get the most +1s and inbound links due to shared content and thus, enjoy higher rankings in the SERPs.
With the same personal Google account, you should be able to create a separate Google+ Page for your business. And to have the Page linked to your website, you have to use the Page's ID instead of your personal profile's ID.