How to display a range input slider vertically

First, set height greater than width. In theory, this is all you should need. The HTML5 Spec suggests as much:

… the UA determined the orientation of the control from the ratio of the style-sheet-specified height and width properties.

Opera had it implemented this way, but Opera is now using WebKit Blink. As of today, no browser implements a vertical slider based solely on height being greater than width. And now that suggestion is under review by WHATWG.

Regardless, setting height greater than width is needed to get the layout right between browsers. Applying left and right padding will also help with layout and positioning.

For Chrome, use -webkit-appearance: slider-vertical.

For IE, use writing-mode: bt-lr.

For Firefox, add an orient="vertical" attribute to the html. Pity that they did it this way. Visual styles should be controlled via CSS, not HTML.

input[type=range][orient=vertical]
{
    writing-mode: bt-lr; /* IE */
    -webkit-appearance: slider-vertical; /* Chromium */
    width: 8px;
    height: 175px;
    padding: 0 5px;
}

<input type="range" orient="vertical" />

Disclaimers:

This solution is based on current browser implementations of as yet
still undefined or unfinalized CSS properties. If you intend to use it in your code, be prepared to make code adjustments as newer browser versions are released and WHATWG recommendations are completed. Subscribe to this github issue to get updates when they finally decide on a CSS attribute to officially control slide orientation.

MDN contains a warning about using -webkit-appearance on the web:

Note: If you wish to use this property on websites, you should test it very carefully. Although it is supported in most modern browsers, its implementation varies. In older browsers, even the keyword none does not have the same effect on all form elements across different browsers, and some do not support it at all. The differences are smaller in the newest browsers.

Despite these warnings, this answer is now nearly 9 years old, and the advice remains largely unchanged.