The library does not have a separate plays section. Plays are found within the literature section (the Ps on levels 2 and 1), 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.