Get another implementation of the same PRNG algorithm, generate a smallish number of longish test cases based on known seeds, and verify that your implementation of the algorithm matches everyone else’s implementations. The more data you test, the more chance it does. If you want to be serious, look into how FIPS validation is done for the algorithm.
There’s no need to test whether the output is random, since far more research has been done on the algorithm by others than you are capable of reproducing.
If you have invented your own PRNG algorithm then you have a rather different problem, because quite aside from testing your code you also need to test your new algorithm. There are various things to do — I think the most important are statistical testing on the output, and peer review by other cryptographers. Basically, though, if you were to design a PRNG algorithm without having enough knowledge in the field to know how to test it, then it will be rubbish.