Fast boats (hydrofoil) travel between Irkutsk and Bol'shiye Koty, all making an intermediate stop at Listvyanka. Schedules and prices can be found on http://www.vsrp.ru/en/passengers/
In Irkutsk, the boats leave from Raketa Harbour.
This is close to Angara dam and is about 4km south of the centre.
Bus 16 takes you there.