Proton-proton fusion in the core produces positrons which are generally seen as part of antimatter, even though you would also need antiprotons (which are not produced) for neutral anti-atoms. The positrons quickly annihilate with electrons to photons, contributing to the power of the Sun.

One simple way is pretty much the same as we use to create anti-protons on Earth -> by accelerating protons and colliding them. With enough energy a proton-antiproton pair might be created. This means for example that solar wind (high-energy protons ejected from the sun) can collide with Earth's atmosphere and the collision can create anti-protons. There were even crazy ideas like: http://www.niac.usra.edu/files/studies/final_report/1107Jackson.pdf