I'm a Swede, a pretty young one at that, and I've been taught since 3 grade about the relationship between Sweden and the Sami: how we expanded into Sapmi in the 17th century, burnt their religious instruments and forced Christianity upon them, exploited them for tax revenue and sent settlers into their lands in the 18th century, confiscated and exploited their lands, made the reindeer-herders the only "true" Sami and tried to erase their cultural identity during the 19th and 20th century. I've seen a documentary about the treatment the Sami experienced during the 19th and 20th century, it covered their treatment in Sweden, Norway and Russia, but I want to know more about how Norway and Russia treated the Sami before the assimilation attempts become so pervasive during the 20th century, how was it for the Sami in Norway and Russia before then?
I can speak on the subject of Russia, mostly pre-18 century.
To put it short, Russians firstly came in contact with Saami in 12th century on regards of the Novgorodian Republic. Republic cosndiered Saami tribes to be valuable assets both in trade terms (because of furs being very common and much needed resource), political terms (Christianization and taxes) and military terms (to use them as deterrence in wars against Sweden and German crusaders). It's important to note that those Saami who pledged their allegiance to Novgorod weren't always converted outright: sometimes only chieftains and their families would be baptized as Christians and used to better govern their subjects while majority of the common folk were left to their paganic beliefs. This happened due to two reasons: first, paganism was very strong among northern Finnic people, and second, unbelievers would be taxed more harshily thus icnreasing profits.
Widespread Christianization of the Saami starts only around 16th century long after Novgorod becomes the part of the emerging Russian state. By bending the knee to the Russian tsar, Saami were from then on considered his direct subjects who would pay his taxes, swear to become proper Christians, serve in his armies, answer his calls for war and be subsequently protected by his troops. Settlements of Saami were a common target for Swedish raids during their wars with Russia in 15-17 centuries. It's also worth noting that Korelians and Saami under Russian jurisdiction around this time refer to raiding parties during multiple Russo-Swedish wars of this time as either "Swedes" or "Germans" even if their opponents clearly were Finns or other Saami, thus completely alienating their western neighbours from themselves so by this time they were more or less considering themselves to be a completely different ethnicity in comparison to other Finnic people.