How do Large particles enter the Amoeba? By what process?

Very simple
Only if you see the topic of endocytosis in a Biology book you will find it completely over there.
First of all there has to be some chemotactic signal generated by the food particles, for this you have to study completely about amoebic stimulationand there nervous system that comprises of a network only not a true nervous system.

Well talking about the ENDOCYTOSIS.endo means inside and cyto means cell... now since amoeba is a unicelular organism u can take as a single cell. It geos towards the food particles.engoulfs it by making a entire circle around it and then slwoly secreting digestive juices(hydrolytic enzymes majorly) and the food particle goes sofetr and gets inside the amoeba and finally further procesing takes place pleading to complete digestion and then excreting only about 2 to 10 % of what it origianlly had eaten.