Essentially, in the case of the Sun (and other stars with a similar interior structure: basically a radiative core and a convective envelope) the oscillation normal modes are stocastically excited by the convection at the envelope of the star. The restoration force is the pressure in the p-modes. There are also other types of modes: the g-modes (whose restoration force is the gravity) are theoretically expected to propagate deep in star but there isn't yet an uncontroversial detection of them in the Sun due to the "noise" produced by convective features.
Take a look at the links at the Prof. Jørgen Christensen-Dalsgaard's web page.