You can apply this CSS to the inner 
:

#inner {   width: 50%;   margin: 0 auto; } 
Of course, you don't have to set the width to 50%. Any width less than the containing 
 will work. The margin: 0 auto is what does the actual centering.

If you are targeting Internet Explorer 8 (and later), it might be better to have this instead:

#inner {   display: table;   margin: 0 auto; } 
It will make the inner element center horizontally and it works without setting a specific width.

Working example here:

#inner {   display: table;   margin: 0 auto;   border: 1px solid black; }  #outer {   border: 1px solid red;   width:100% }
   
Foo foo
 
EDIT
With flexbox it is very easy to style the div horizontally and vertically centered.

#inner {     border: 1px solid black; }  #outer {   border: 1px solid red;   width:100%;   display: flex;   justify-content: center; }
   
Foo foo
 
To align the div vertically centered, use the property align-items: center.