Is this a proper past tense?
Today I've darkened 59 appropriate circles.
That sentence is grammatically absolutely correct. I’ve darkened is indeed one kind of past tense; specifically, it’s what’s known (depending on how technical one’s being) as the perfect tense or the simple present perfect tense, and also by various other terms. Expanding it to I have darkened, have is an auxiliary verb, and darkened is a past participle.
The sentence is also completely confusing out of context — I have no idea what it’s supposed to mean. Was that deliberate? I’m reminded somewhat of Chomsky’s “colourless green ideas sleep furiously”. Edit: Stuart Bentley in comments points out a very plausible context.
Strictly "I have darkened" is a perfect tense using the past particple; some people would call it the present perfect. By contrast, "I darkened" would be a past tense; some people would call it the simple past and others the preterite.
Wikipedia has an article on past tenses.