The library does not have a separate plays section. Plays are found within the literature section (the Ps on the second floor), which is organized by nation, time period, and then author. This arrangement means that works by a playwright could be next to a fiction writer or a poet, so browsing for plays is a bit difficult.
If you don't have a particular playwright or play in mind, the general literature section and each national literature section have a call number area for collections of plays. Try browsing in the following areas:
Russian: PG 3240-3255
If you are looking for a particular play text, it might be published in one of several ways: full playscript published separately, in an anthology on a particular theme or covering a particular time period, in a periodical, or on the web. Each of these publication types has a different search strategy for finding the text (see below). Also keep in mind that some plays are never commercially published.