To add a new post, tap the bacon icon in the upper left and then tap the action sheet (pencil and paper) in the lower right of the menu.
Select whether your post is a Link, Text (self) post or Photo. Add the content of your post and the title and subreddit you are posting to. You can flag your content as NSFW (not safe for work) if necessary.
Once you're done, tap "Submit" in the upper right hand corner of the screen.