The exams of the actuarial societies are as important to becoming an actuary as the CPA is to becoming an accountant or the bar exam is to becoming a lawyer.
All students should try to get at least one, if not two, or even more exams done prior to graduation. The more the better (although anything more than the first three or four leads to a problem of diminishing returns - don't expect to get paid the same as someone with the same number of exams and more work experience).
Understanding the exam process is necessary: The easiest thing to say about the actuarial exams is,
THEY ARE NOT EASY.
Most exams have very low pass rates, compared to what you might expect: The September 2005 Exam P (the first exam) had a 36.8% pass rate (September 2005 Examination Results).
Having said that, preparation is key, just like any regular exams for college courses. If you put in the necessary preparation with the necessary texts, you should pass with room to spare.
The object in taking the exams is to either, in the SOA, attain ASA (then FSA) certification, or, in the CAS, attain ACAS (then FCAS) certification.
Also, if you pursue a career in pensions, you will eventually need to take the EA exams.
Now, for the detailed explanations:
First, there is a difference between the Casualty Actuarial Society and the Society of Actuaries. Although they jointly administer Exams P/1, FM/2, and C/4, the CAS offers Exam 3, which the SOA does NOT accept as credit towards the preliminary requirements (on the other hand, the CAS accepts Exam M). After the first four preliminary exams, the societies are completely different.
Note that Exams FM, M, and C are changing in 2007, with the addition of Financial Economics (pdf).
EA Exams - for Pension Actuaries
Here are application forms [pdf] for the SOA exams and CAS exams.