You can go to the Google+ help pages and search for codes that you can place on your pages. If you have blogger, you could search for a Gadget that you can add to your Blogger.
You can do this if you have a google page. Not your personal google+ but a google page for your brand. When you have a google page set up, you will link your site and a pop up will show with a code and instructions on how to link it to your site. That's it!
Hey for web design which platform you are using? To integrate your Google + page to your site you just need to create business page of your site on profile and then link that page to your site. You need to add a publisher tag on your home and just place your profile link in that tag. Once you tell me platform of web site development i will let you know more.
In WordPress, In profile section there is option to update you Google + profile and then you need to add your blog page in profile of particular user who is adding post on your site.
I can understand building a brand page if you have product or are a big company, but how do you properly use a business page for a blog you are trying to market? Do you turn your business page into your newsletter or something?