Accommodation mechanism.
I think the problem you're having is in the way you're thinking that all contracted muscle shortens, and all relaxed muscle lengthens. But the cilia is different. The ciliary muscle is a circular or radial muscle (like the orbicularis oris of the mouth.) Thinking of it like a sphincter muscle is much more helpful.

The ciliary muscle is attached at its periphery to the lens by suspensory ligaments (aka the zonules). Think of the the lens, the suspensory ligaments, and the ciliary muscle as a single unit with only two components whose length can change dramatically: the cilia and the lens. The length of the suspensory ligaments is more or less fixed.

This may be counterintuitive, but for seeing at a distance, the ciliary muscle relaxes, and the muscle in effect becomes "thinner" (think of the capitol letter O in a thin font, or think of a shpincter muscle; when the latter relaxes, it becomes thinner and more spread out). This means the "decreased distance" taken up by the ciliary muscle must be made up for by the suspensory ligaments and the lens: The tension on the suspensory ligaments increases, causing the lens to assume a flattened shape.

For near vision, the opposite occurs; The ciliary muscle contracts (think of the letter O now very bolded - it takes up more of the fixed distance.) This allows the ligaments to relax, allowing the lens to assume a more rounded shape. 

Does that make any sense at all? I hope so, because it is essentially how it happens.

I did find a YouTube video; unfortunately it explains it pretty much like I did varying in a few details.

Morphological Study of the Accommodative Apparatus in the Monkey Eye Way way complicated; it's better to just believe me.