To display any random post always in the homepage of the blog
First Goto Posting-->New Post
See the bottom of the page Post Options  will be there near labels
click that  Post options then see on right side

The below option will be there with Automatic checked,change the checked option to set date and timethen change the day and date to current day and date,then publish the post and open your homepage the post will be there in home page.You can also change reader comments option here.