Unfortunately, students are caught cheating with some frequency at UCSD. In the math department, this most often takes the form of cheating on an exam: having a ringer take the exam, copying others' exams, or changing an exam and then resubmitting it for a regrade. (There is also occasional copying of work on Matlab assignments; in the past, professors have usually chosen to deal with these infractions without pressing formal charges, but you should talk to your professor to determine their individual policy.)
It's important to try to stop academic dishonesty before it happens. Such steps may include:
Making sure students understand the policies of the class regarding dishonesty, and attempting to foster in them the importance of integrity.
Proctoring vigilantly.
Having a policy in place for returning exams and handling regrade requests.
If, despite all these safeguards, you suspect a student has cheated, take the following steps:
Get the instructor of record and/or fellow TAs to confirm (independently, if possible) your observations.
Gather evidence to support your claim. Note as many details as you can, as they may be important later.
Tell your instructor of record about all this as soon as possible.
You or the instructor of record should fill out a report form as soon as possible. Forms can be found here.
Ultimately the instructor of record will decide what to do next. They may bring forth formal charges, in which case you may be asked to testify later in a hearing. For more details about the official process after a charge is made, and for what officially constitutes cheating, see here.