The DNA and the mechanisms for reading the information in the DNA molecule are located in the nucleus. The initial process of breaking down glucose to release energy remains in the gel-like cytoplasm , as in prokaryotes. But, additional, complex processes which breakdown molecules further are located in the mitochondria . And, plants have the process which capture light energy and store it, photosynthesis, located in the chloroplasts . Mitochondria, chloroplasts and nuclei all have two membranes surrounding their interior.
Many eukaryotic organisms are single celled, like the amoeba.
But, of course, all the animals and plants are comprised of these complex eukaryotic cells. The cell is a very dynamic entity. Molecules are zipping back and forth along the microtubules and microfilaments. Materials are being broken down and others are being manufactured. Worn out molecules, mitochondria, chloroplasts, and materials taken in from the outside are being broken down.