The relentless Atlantic waves draw surfers to Sagres like moths to a flame. The angle of the headlands means some beaches are much more sheltered than others, making the surfing appropriate for a wide range of skill levels.
If the surf isn't much good on one of Sagres's four main beaches, it's worth taking a look at the others—conditions vary significantly between them, depending on the wind and tides. You can also head slightly northwest of town to Praia do Beliche, another popular surfing spot.
There are several surf shops in Sagres, and lessons are relatively inexpensive. It's also possible to hire whatever gear you need from the stores, avoiding the hassle of transporting it.
If being dumped by waves all day isn't your idea of a good time, kitesurfing is another good option. It's probably best left to those with prior experience, however, as the wind can be strong and very gusty.