Buses from Kargopol to Lekshmozero (R150, 1¾ hours) depart at 6.15am and 5.15pm on Tuesday and Friday, returning roughly two hours later. In springtime the unpaved road is impassable by bus. Taxis between Kargopol and Lekshmozero cost R2000 one-way.
It's around 10km from Lekshmozero village to the entrance of the national park itself, where no cars are allowed. You can hike, cycle, or take a taxi there for around R350.