There are a number of statistical tests that are designed for this purpose. The Chi-squared and Kolmogorov-Smirnov tests are two of the better known ways.
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Experimental probability is obtained by repeatedly carrying out an experiment. It is the ratio of the number of favourable outcomes and the total number of experiments. Theoretical probability is calculated from a model of the experiment using the laws of physics or nature (or whatever).
The theoretical probability provides a model for predicting the outcome of trials. You then carry out a number of trials. Compare the outcome of your trials with the results predicted by the theoretical model. The comparison will usually involve "hypothesis testing", a branch of statistics. This is a method to test how likely the actual outcomes are if the theoretical probabilities were true. The exact nature of the test will depend on the theoretical basis and so the answer cannot be simplified.
In theoretical probability, the probability is determined by an assumed model (for example, the normal distribution). (compare with empirical probability)