I’d suggest subscribing to their blog (bloggers always appreciate that) and then I would contact them through the comment feature and mention that you write for the same niche and would be interested in writing guest blog posts for them or in exchanging web links with them (where you link to their blog and you link to theirs. Also ask them for advice. Bloggers are usually glad to help newbies. 

Once you have established the relationship, suggest emailing them new posts for their possible use on their blog, too.

I’d also tease your blog posts on Twitter and when you eventually get on Facebook and LinkedIn,post teasers to your blog posts there as well, especially into relevant Facebook and LinkedIn groups.

Kathy BernardGetajobtips.com