How to sort the post to a specific category

wp_query() is good option to show list of post in wordpress. If you want to show post of certain category then it can be done by using category's ID Or by Category's slug.

$paged = get_query_var('paged') ? get_query_var('paged') : 1; 

$args = array(
    'post_type' => 'post',  //Specyfying post type
    'cat'=> 1,    //Selecting post category by ID to show
    'posts_per_page' => 10,  //No. of posts to show     
    'paged' => $paged       //For pagination
);

In above code I am showing category whose ID is 1 (‘cat’=> 1,).
If you want to show multiple categories then use code like this

'cat'=> '1,4,6', 

In above code 1,4 and 6 are ID of different catogories.
If you want to leave any category then add minus in front of ID like this

'cat'=> -5, 

If you want to call category by slug instead of ID then show it like this

'cat'=> 'type_slug_here',

After specifying array we will use wp_query() and while loop to show list of posts.

$loop = new WP_Query( $args );

while ( $loop->have_posts() ) : $loop->the_post();
    //To show Title of post
    the_title();            
    /*****     Thumbnail     ******/
the_post_thumbnail(
array(120, 90),   //Width and height of featured image
    array(

    'class' => 'thumbnail',   //class to apply css properties
    'alt' => 'post thumbnail', //Alternate text if there is no image to show
    'title' => 'my custom title' //Title to specify
)
);
/*******     Thumbnail Ends   ********/

//Show description of post  
 the_content(__('Continue Reading'));
endwhile;

For more/brief detail read this article. This article describes all detail about listing post But if you want to read only about showing one catogory right now then find heading with name "Category Parameters".

How to find Category ID

In case if you don’t know "how to find ID".
Go to Dashboard -> Post -> Catagories. There you will see all available categories (you can also create more categories there). You can find category ID by
1. Hover on category name then 4 option will appear. Click on edit option, In edit page you can see ID in url.
2 Or simply hover in catogory then hover on edit option, By hovering on edit option you will see url at bottom left side of page. You can see ID there.