I am impressed with the way people ride their snow scooters up here, the way they jump on and off their sledges when the sledges get stuck in the snow and the way they know exactly how cold you are going to be even with three layers of clothes if they are not the right type and quality designed for the Northerner's lifestyle.
My fondest memory of the Sami outdoor lifestyle is probably captured by two of the pictures below: two old women getting ready their snow scooter and leaving with high speed followed by their dogs. What a life! :)
Kautokeino is "in the middle of nowhere", so for the average person there's only one way: the highway. National road 93 runs from Alta to the Finnish border. It's 130 km to Alta (north of Kautokeino), 40 km to Finland (south of Kautokeino), 70 km to Hetta (Enontekiö), Finland.
If you're not driving, and don't want to spend tons of money on a rental car, helicopter or personal airplane, there's a bus going from Alta every two days. There's also a bus from Karasjok (110 km east of Kautokeino)