This report not abot Valaam as such but the options and technicalities of getting there.
The closest mainland point is Priozersk, three hours from St. Petersburg by train. Trains leave St. Petersburg from the Finland train station, Metro Proshad Lenina – Finlyandsky Vokzal. Apparently there are overnight boats direct from St. Petersburg but I have no details. This story is mostly about getting from Priozersk to the Valaam Archipelago (Finnish: Valamo) itself.
A clear and to the point description of how to get there and where to stay is on the Valaam Monastery site.