How do legs of tiny insects/spiders like mosquito/Opiliones work?
Arthropods use basically the same system to operate their legs. Yes their legs are tiny, but so are their muscles.(Is it so hard to imagine everything is downscaled? Their digestive system is also much smaller, but they don't need to eat the same amount as we do either...)
In general it's just a kind of smaller-sized mechanism that is based on the same principles: use a muscle to create tension over a joint, and so move the appendages. The big difference is off course that in mammals the muscles work against an internal skeleton, and in arthropods the muscles attach to the inner surface of an external skeleton.