Across from the town of Monroe, along the east side of the river, upstream of the dam, along an access road, there is a place you can hand launch small boats.
Be aware that the dam is a couple of blocks to the North (downstream), and you don't want to go over. Also, the Long Tom river flow is low and peaceful in the summer, but it can be changed by the Fern Ridge Dam gates. Information on Fern Ridge outflow is available.