You can log into Omnibear using web sign-in. This allows you to verify that you own the website you want to post to. There are a number of ways you can implement web sign-in on your site, but the easiest and most common is through indieauth.com.
Omnibear posts to your site using micropub. Micropub is a web protocol used to create, update, and delete posts on your website using third-party clients (apps). It is an open specification published by the W3C along with other emerging social web protocols.