Geordie Williamson has a very nice set of notes on perverse sheaves: http://people.mpim-bonn.mpg.de/geordie/perverse_course/lectures.pdf it deals with some examples on curves (section 10).
You can also look at De Cataldo and Migliorini's paper (section 2.2): http://www.ams.org/journals/bull/2009-46-04/S0273-0979-09-01260-9/S0273-0979-09-01260-9.pdf