Lake Baikal is the deepest lake and holds 20% of all drinking water in the world. It's a precious gift of nature and has to be protected. Because of that there is not much touristic infrastructure built around it. The most touristic seems south western part around the town of Listvyanka. It's quite easy accessible by public bus from Irkutsk main bus station (Avtovokzal - Автовокзал). Ride takes around an hour and cost 120 RUB. There are busses all day.
But there are more peaceful areas. His article shows hos to get to he island of Olkhon on budget.
The cheapest way to Olkhon is of course by hitchhiking which is extremely easy in Russia. I made almost 7000 km by hitchhiking in Russia and don't have negative experience.
But there are also minibuses that go from Irkutsk main bus station (Avtovokzal - Автовокзал) to Khuzhir. Khuzhir is the biggest town on the island. There is a lot of private companies that offer minibuses for 700-800 RUB but there is also an Irkutsk city transport minibus for 510 RUB and presents the cheapest option. You buy the ticket at the bus station. I recommend doing so a day before, because they might be overbooked if you go there in the summer. There are only three busses per day, departing at 8:30, 9:30 and 10:30.
Price of a bus ride inside of city limits of Irkutsk is 15 RUB.
Going on the island the bus must get on the ferry. Also the roads are bad. There is a good road only until about the half way to the ferry, then it gets worse and worse. On the island there is no paved roads at all. This means the duration of the ride can be anything between 5 and 7 hours.
When you arrive to Khuzhir, bus drops passangers off at the bus station. The only thing is that not even with a great imagination I couldn't guess it's a bus station :) It's just a spot on some street besides a general store where busses stop.
Anyway you're in Khuzhir and can start exploring the area.
Let me mention also about the accomodation. There are some nice western style hostels in the town. You can book them in advance over the internet.
But much cheaper option is to find something when you're already there. Just by walking around the town you'll see a lot of houses with large letters "КОМНАТЫ" written somewhere. It means rooms. The expected price per night is around 400 RUB for two or three bed room. Don't expect commodity, but it can do for a night or two if you want to save some money.
Third option is wild camping. But check the temperatures at night for the requested period. In Siberia days can be very hot but the nights get freezing cold.
For the way back you take the mini bus from the same spot where it droped you off on the way there. The price is the same (510 RUB) and the last one departs at 10:30. Although there might be private minibusses later on. But they cost 100-200 RUB more.
1. Take Irkuts city bus to main bus station (Avtovokzal - Автовокзал) - 15 RUB
2. Take minibus to Khuzhir - 510 RUB (8:30am, 9:30am, 10:30am)
3. Enjoy beautiful Baikal (for rooms search "КОМНАТЫ")
4. Take minibus back to Avtovokzal Irkutsk - 510 RUB (10:30)