(Description thanks to jetmanjake, davefriend, and JeffB from RapidsRiders message board.)
Some grade I-ish paddling can be cut if you put in at Aitkin County Park, about 5 mi north of the jct of highways 65 & 27. The park entrance is a clearly marked dirt road that runs east off Hwy 65. Stay left when on the dirt road to eventually get to the park. It is 2 to 2.5 miles off the highway.
The take-out is found by going east on 360th Ave and then turn left when 360th ends in a T intersection (approx 5 mi). After the left turn, go until you reach a bridge crossing the snake (less than a mile). 360th Ave is the dirt road that runs east from the junction of Hwys 65 & 27. (Hwy 27 runs west and is paved.) This junction is the village of Woodland - a bar and couple of buildings on the west side of Hwy 65.
All wheel drive may be an asset at times since the unpaved roads can be rather mushy.
The two significant rapids (Upper and Lower Snake River Falls) are both signposted, scout both river left. The term "falls" is a definite over-statement. Still they are fun sections with the river at about 3' or so. The first is a ninety-degree left hand turn against a wall, the second is a gorge-y bit that forms a couple holes, maybe III- at medium flows. While you'll paddle some fairly long stretches of flat water, Lower Falls is a fairly continuous rapid, maybe 900 yards worth. Since this stretch is paddled often in open canoes, both rapids are well posted with portage trails for those not inclined to run it. The rest is a good beginner/canoe run with I-II riffles.
Minnesota DNR has a web page with pdf maps at
DNR Canoeing - Snake River. The "top left" pdf shows the section of the river we are talking about in a scaled up inset. Note that the pdf calls 360th ave "County Road 82" and/or "State Forest Road". I've never seen signs in the area with those designations. Likewise, the pdf map calls Olympic St. "County Hwy 23". I don't recall that there is any kind of signage for this road...