Utsjoki is by its population a very small municipality and the only one in Finland having Northern Sámi speaking majority (in 2019), even though the language balance is extremely 50/50. Tourism in the municipality is centered around salmon fishing during the summer season but the Kevo trail is an important attraction as well. Commercially Utsjoki municipality is much, much more connected to Norway than to Finland.
Technically all inhabitants live in the river valleys of Inarijoki-Teno and Utsjoki. This means that the vast majority of the municipality area is actually just uninhabited tundra... which it is! Notice this when you are trekking.
Practically, the only way to get to Utsjoki is using the roads; either driving or travelling with the bus. Remember that distances are huge. There are two daily connections from Rovaniemi to Utsjoki village and Nuorgam village, and one connection to Karigasniemi village. The trip takes about 7 hours and the price is approximately 80 euros!
One can reach Utsjoki using E 75 from the south and E 6 from Norway. E6 passes 4 km (3 mi) north of Utsjoki, on the Norwegian side of the border.
The closest airport is in Ivalo. There are bus connections available but only by request! Matkahuolto has connection from the Ivalo bus station, not from the airport.
There is one single bus connection from Karigasniemi village to Utsjoki village and back every Mondays and Thursdays. See timetable here. Otherwise you must use Matkahuolto bus connections or taxi. Or rent your own car. There is very little traffic on the roads so at the summertime a bicycle is also an option but, please, do understand the distances.
Consider hichhiking twice. It shouldn't be too difficult to arrange your trip beforehand with some local if necessary.
Ask your accommodation site for options to get around!
There are no major tourist attractions in Utsjoki so tourism is of minor scale. The main village Utsjoki is an administrative centre but has quite a little services but a shop and a restaurant. Even the downtown's only hotel became closed few years ago. Instead the villages Karigasniemi (about 100 km SW) and Nuorgam (about 70 km NE) have variety of tourist services including Alkos(!!!). Nuorgam is the very northernmost village of Finland and is frequently visited by thirsty Norwegians.
NOTE: Fishing salmon from any part of the Teno river system is NOT an everyman's right. You need a permission. Fishing without a permission or not following the regulations for fishing will cause fine and loose your catches.
NOTE: To prevent microscopic Gyrodactylus salaris organism from getting into the Teno river system, there are extremely strict regulations considering biosecurity risks in any part of river Teno. Make sure you have official documents that your fishing equipments are sterilized as they must be. For Teno river fishing see here.
People coming from the Norwegian side of the border usually head for the Alko store in Nuorgam or Karigasniemi to buy liquor, because it's far cheaper than in Norway. Tourists from elsewhere will probably find other activities more interesting.
There are no nightclubs in Utsjoki. Maybe you may join locals to visit closest party places in Karasjok, Norway.
Visit the nearby village of Tana in Norway. Remember to buy your alcohols from Finland as it is much more expensive in Norway.