what steps occur in the process of phagocytosis?

Firstly, a foreign pathogen will enter the body and produce chemicals that attract the phagocytes. The phagocytes will recognise this non human protein and engulf and enclose them into a vesicle to form a phagosome . A good analogy to think of here is pacman moving around and eating stuff! The phagosome will combine with a lysosome to form a phagolysosome. Its important to remember here that lysosomes are full of 'degradative enzymes' which simply means they destroy things. So the lysosome will then digest and destroy this pathogen. This is part of the non specific immune system.