The closest gateway to Lake Baikal from Irkutsk city, which lies on Trans-Siberian Railway, is Listvyanka village. There are few daily local buses from Irkutsk bus station to Listvyanka village. When you are there, you can enjoy the view on Lake Baikal and\or hike on Great Baikal Trail, which goes along the lake.
I did this in May 2016. After one night in Listvyanka, I started hiking on the trial Listvyanka — Bolshie Koty (east from the Listvyanka village).
On the way between Listvyanka and Bolshie Koty, there is a camp site for your tent. There is no accommodation.
More info about Great Baikal Trail: http://greatbaikaltrail.org/en/node/1436
GPS coordinates of Bus station in Irkutsk for bus to Listvyanka village: 52.2896065, 104.3047588
First day of the trek was sunny, but next day, the weather went wrong. It was raining and very cold, almost snowy. I realized that May was too soon, and better would be trek there in summer months (July, August).
=== Knaper ===