How does an eunuch pee?

Through his urethra just like anyone else.

Various cultures applied different degrees of mutilations, some removed both penis and testicles, others only the testicles.

With only the testicles removed, urination is as it was before.

For those who applied full amputation, some sort of pipe or small tube was usually inserted into the urethra to allow urination during healing.

There's some report that eunuchs would continue using a tube for that purpose even after healing as a means of achieving a directed flow.