Solo parts
If you have a solo part for a transposing instrument in PlayScore it will play in the written key by default.  To hear the music at concert pitch you should set the transposition on the Staff settings screen.  For example for a Bb clarinet set the transposition to -2.
Tip: selecting an instrument from the dropdown only affects the timbre.  It does not set a transposition.
Music with an accompaniment or ensemble music
If your music has instruments with different key signatures, for example Bb clarinet and piano, turn on Auto transposition under the cogwheel.  PlayScore will then adjust everything so that the instruments sound right together.
You should set Auto transposition if you want PlayScore to accompany you by playing the piano part while you play the clarinet for example.
To make PlayScore pick up transposing information from instrument names in the score turn on Lyrics and text under the cogwheel
For more information on transposing instruments, especially ensembles involving transposing brass, see Transposing instruments and transposition in the Help section.