How to display posts on custom page without declaring a posts page in reading settings?

Because you have not write any description function, thats why you are not getting any description of posts. This function is use to call the description of posts

the_content(__('Continue Reading'));

ABove function will show you complete post description But if you don’t want to show whole post description and only want to show excerpt (few lines of description) then use this function instead

the_excerpt();

This function will show you few lines for posts. Add one of these function inside while loop (before endwhile;). To be more clear in you code the_title function is use to display the title of post and the_time and the_author function use to display post publish time and author of posts respectively. Add my given function after the_title function line or after the_author function line as per your requirement.