Answer
The nucleus contains the cell's chromosomes and is the genetic control center of the cell. The nucleus looks like a large dark round dot under microscope.
The mitochondrion synthesizes ATP (powerhouse of the cell). Mitochondria are smaller than the nucleus, come in a variety of shapes, and tend to squirm. Their texture looks a little rough/wavy.
Lysosomes are packages of enzymes bound by a membrane. These enzymes are responsible for breaking down and digesting things (bacteria, glycogen, organelles, etc). They are often roundish and have dark grey contents and are devoid of structure.
Centrioles are dark, short, cylindrical objects in the cells. There are often two of them right next to each other. Centrioles play a key role in cell division.
Work Step by Step
The nucleus is the brain of the cell, the mitochondria are responsible for ATP, lysosomes contain enzymes for digestion and break down, and centrioles help with cell division.
When looking at a cell under an electron microscope, look for the nucleus first. The nucleus is often the biggest, darkest round thing you can see. The mitochondria are irregularly shaped and have an almost roughen texture to them. The lysosomes will appear as little spherical bubbles. The centrioles are little dense packages and always come paired. If you see more then two little dense packages, those aren't the centrioles.