The same general tactics that you would use for any blog would apply. Try guest posts, commenting, pinging, and SEO. SEO is a bit more difficult than it would be having your own domain, but it is possible.
As explained in this blog post (http://grandadmiralgamez.blogspot.com/2014/09/when-should-you-ping-your-blog.html) pinging is when you let search engines, blog directories, news sites, etc. know that you have updated your blog, and makes it easier to find on the Web. There are numerous pinging services such as Pingle, Google Pinger, Pingomatic, and so on. You can search for them using your favorite search engine.
What is your blog about? Niche or topic specifically? I suggest you join on blog communities relevant to yours. Then add a social media share button on your contents. If you have a social media account like facebook join on groups relevant to your niche and share your content. Bookmark your contents through reddit and stumbleupon. Don't forget to use enticing images or videos that will catch people's attention.
Just share your blogs on all social media websites like Facebook, Twitter, Linkedin, Pinterest, Tumblr, Scoop, Facebook Groups etc... Pinging your blogs, bookmarking, web 2.0 submissions etc. Link your blogs with internal and external blog keywords. It will surely increase your blog traffic.
If you have a social media account like facebook join on groups relevant to your niche and share your content. Bookmark your contents through reddit and stumbleupon.