The above node has probably excellent account of sami history
(I didn't know nearly as much, and I'm one...), but is a bit thin on how they live today. I might not be the best to tell about it, since I basically abandoned the sami culture
some years ago, but I don't see anyone else around... (by the way, the actual spelling is Sámi. The 'á' is one-and-half 'a'. I'm used to "Sami", and it's also the spelling used in Sámi Radio
webpage at www.yle.fi/samiradio)
First, The Saami do not consider themselves citizens of these nations. At least here, in almost northernmost finland, the heart of finnish sami territory, this is certainly an exaggaration. It's not like we live in reservations, wear our national costumes all the time or have our own secret societies plotting to overthrow local government and found a Sami nation. Most of the time it's really hard to even tell who is Sami and who is a colonist, as the two have mingles for a while. Nobody around here makes a big deal out of it that I've seen, and considering yourself not to be a finn is certainly not the case. Technically, we are citizens of Finland too. There's this legal body (Saamelaisparlamentti - Sami parlament, I think), but for what I've heard, it really doesn't have that much power.
Now, as for the culture, that is more to the point. Many still practise a form of the traditional reindeer tending, but I don't think it's primary (or the only) source of income to many. Wasn't to my family, in any case. People own their reindeer and they do feed them sometimes when food's scarce and come to these events called poroerotus (separating the reindeer) and vasanmerkintä (marking the calves) to gather all the reindeer in area to one place, to separate and account their own ones, take suitable ones to slaughter, to mark the newlyborns as their property and like, but I understand mostly they just let reindeer do on their own in the woods as much as possible. Note that my information on this is a bit unaccurate as I never did learn that trade either.
In other related thoughts, the "Save the Wolves - Shoot the Saami!" is probably not exactly racism. Very likely it refers to same controversy that is going on here in Finland - wolves eat reindeer, thus cutting on Sami's income, but there are laws against killing them (if you ask which you need to raise your humor budget). Some Sami kill the wolves anyways, which has understandably pissed off a lot of people - there aren't that many wolves around even without Sami killing them.