For invasive pathogens the only way to survive, and consequently make you sick, is to get inside your cells. This is a rough exercise as you have an immune system working everywhere in the body to prevent this and the cell to be invaded is none too happy with the idea either so invasive pathogens must use tricks.
After evading or surviving the immune system, another post for another day, some exploit a mechanism called receptor mediated endocytosis (RME), in which the pathogen binds to a receptor on the cell triggering the cell to alter its shape to internalise the pathogen. RME is used by cells to recycle extracellular components but it a pathogen can make itself fit the receptor instead it can trick the cell into giving it free access to its insides.
Another mechanism, commonly employed by membrane bound viruses, is membrane fusion. Given that membrane bound viruses contain a secondary structure called the nucleocapsid, which houses the genome, they can fuse their own membranes with the host cell which results in the nucleocapsid's release into the cytoplasm.
|(a) HIV entry by fusion and (b) receptor mediated endocytosis of light blue dots ((a) modified from credit and (b) modified from credit|