Does a person experience release of dopamine while doing something she/he enjoys? I am wondering if a person would experience an increase in the level of dopamine while doing something she/he enjoys such as playing guitar or reading a book. And what are some other neurotransmitter that would be released?
Like many topics in neuroscience, this is a controversial subject.  While dopamine is very popular among the public as a mechanism for pleasure, recent research challenges that view and has started to tease apart pleasure from motivation, finding a distinction in dopamine.

John Salamone's opinion:


  Low levels of dopamine make people and other animals less likely to work for things, so it has more to do with motivation and cost/benefit analyses than pleasure itself.


and his peer reviewed research:

Salamone, John D. and Correa, Merc. (2012).  The Mysterious Motivational Functions of Mesolimbic Dopamine.  Neuron, 76:3, pp.470 - 485.

It's more likely that the experience of pleasure is a distributed circuit phenomena, not down to any one neurotransmitter:

Smith, Kyle S.; Mahler, Stephen V.; Peciña, Susana; Berridge, Kent C.
Kringelbach, Morten L. (Ed); Berridge, Kent C. (Ed), (2010). Pleasures of the brain. , (pp. 27-49). New York, NY, US: Oxford University Press, viii, 343 pp.