Reporting d-prime results

d-prime values are usually fairly well normally-distributed. So you can use any parametric test relying on the normality assumption (in facts you should always z-transform fractions before to use a parametric test on them). If you have only 2 conditions you can use a classical t-test. From your question it seems you have only 1 value per participants so that would probably be an independent t-test. If you have more than 1 comparison an ANOVA would be the typical test to use.

For reporting results it is a bit tricky. d-primes are not that intuitive for people. So you might want to report fraction correct in the text, but run your tests on d-primes. For the same reason you might want to plot your results as fractions. Below is an example of wording (but refer to a statistical textbook for conducting and reporting statistical tests). Note that it is fine to report means and standard deviations of fractions. However parametric tests should always be conducted on z-scores. I know people use fractions in tests all the time but it is wrong.

The mean recognition rate increased from NN% to NN% between the conditions ... and ..., for a mean improvement of NN ± NN% (SE). This difference was significant in an independent t-test on z-transformed recognition rates: t(N)=N, p