Does PCA change the values of the data? Principal Component Analysis is a means to reduce the dimensionality of data, if I understand correctly. 

So if I have a 1000 sample point 12 dimensional matrix and reduce it to a 1000 sample point 2 dimensional one, then are the values of the sample points themselves changed in some way? or are simply 10 dimensions/columns thrown out and 2 of the original remain?
Yes, the new 2 dimensional values will be a projection of original 12 dimensional points onto the two principle components (vectors). 

please refer to the first figure in this clear tutorial:
http://lazyprogrammer.me/tutorial-principal-components-analysis-pca/