How do I vertically center an H1 in a div?

You can achieve this with the display property:

html, body {
    height:100%;
    margin:0;
    padding:0;
}
#section1 {
    width:100%; /*full width*/
    min-height:90%;
    text-align:center;
    display:table; /*acts like a table*/
}
h1{
    margin:0;
    padding:0;
    vertical-align:middle; /*middle centred*/
    display:table-cell; /*acts like a table cell*/
}

Demo: http://jsfiddle.net/a3Kns/

you can achieve vertical aligning with display:table-cell:

#section1 {
    height: 90%; 
    text-align:center; 
    display:table;
    width:100%;
}

#section1 h1 {display:table-cell; vertical-align:middle}

Example

Update - CSS3

For an alternate way to vertical align, you can use the following css 3 which should be supported in all the latest browsers:

#section1 {
    height: 90%; 
    width:100%;
    display:flex;
    align-items: center;
    justify-content: center;
}

Updated fiddle