There are different ways in which you could land yourself a guest posting gig on different websites. I happen to be familiar with two methods, which are very effective and have landed me quiet a few gigs in the past.
The first method is probably the oldest way of soliciting to work for any organization. All you have to do is visit the target website and surf the contact page. After that, you can contact them via mail with your solicitation. But note, this methods mos times needs regular follow ups as it might take a while before you receive any form of notification or response.
The second method is the most modern process and probably the fastest proving way of landing a writing gig. The first thing to do in this method is to search and register with any reputable freelance writing sites. There's hundreds of them on the internet. An example of such site are Guru.com, Freelancer, etc. After registering with any of them, you could simply find available jobs in the market place posted by websites who are in current need of specific writing jobs. This method is more reliable as you get paid instantly on the site after completing and submission of work done. It's more like fiverr, only that these new sites have more available jobs with equal opportunities to both beginners and old timers.
It should be noted that the host websites as explained above isn't the provider of jobs, they only connect employers with employees.