If you do not assign Categories to posts they cannot appear on them. If you do assign them to posts then when the posts are on your front page or whichever page you use for displaying posts they will appear on them.
There is only one dynamic page in a blog for posts and we cannot post to more than that one page. But we can create the appearance that we have posted to more than one page.
We organize our posts by assigning Categories to them. When we publish a post it automatically appears on the running page for posts and also on the Categories pages and Archives pages. Note: There must be one published post in each Category in order for there to be anything to display.
A custom menu allows you to display Categories in tabs along the horizontal navigation where normally only Pages tabs are displayed. If you wish you can also include Pages and custom links in your custom menu as well.