The Nucleus
The nucleus is where most of the genetic material (genes, DNA) is housed. It is enclosed by a two layered nuclear membrane which is perforated by pores which regulate the passage of molecules and particles.

Within the nucleus is the nucleolus which makes the ribosomes.

Ribosomes
Ribosomes are the cites of protein assembly. Prokaryotic ribosomes are smaller and different than eukaryotic ribosomes. Some antibiotics exploit this difference.

The Endomembrane system
Many of the membranes of the eukaryotic cell are part of this system. The endomembrane system includes: the nuclear envelope, endoplasmic reticulum, Golgi apparatus, lysosomes, vacuoles and the plasma membrane.

Endoplasmic reticulum (ER)

The ER is a membranous labyrinth containing more than half the membrane found in a (eukaryotic) cell. The tubules and sacs of which it consists are separate from the cytosol and continuous with the space in between the two layers of the nuclear envelope.
ER functions in the synthesis of lipids, carbohydrate metabolism, and detoxification of drugs and other poisons.
ER attaches hydroxyl groups to toxins, making them more soluble and easy to flush out. This takes place in the liver. Increased "tolerance" to drugs and alcohol results in part to an increased production of smooth ER to cope with the extra burden.
ER also is where the secreted proteins are synthesized. Once the secretory protein is formed it gets wrapped in a transport vesicle
One of the functions of the rough ER is to make membranes. These can then be used as transport vesicles that go off to other parts of the endomembrane system.

Many transport vesicles from the ER go next to the Golgi apparatus. Stuff from the ER comes here to be finished off, stored, and shipped out in vesicles. Secretory cells have loads of "Golgi bodies".
The golgi apparatus puts molecular ID tags on the vesicles so that they will be recognized by their targets.

A lysosome is a membrane bag filled will hydrolytic enzymes which digest macromolecules. There are enzymes designed to digest all the various classes of macromolecules which we have covered. These enzymes work best in an acidic environment about pH 5. We could not have this going on at large in the cell.
Lysosomes are used in recycling a cell's own organic material.

Vacuoles are large vesicles. There are food vacuoles and there are contractile vacuoles which pump water. Plant cell vacuole, central vacuole, is used for storage of various compounds (hydrolytic enzymes, wastes, pigments, poisons). They also help the cell become larger without adding a lot of cytoplasm.

Mitochondria
Mitochondria are found in nearly all eukaryotic cells. They are the site of cellular respiration, where ATP is generated from sugars.

Chloroplasts
Chloroplasts (found in plants and algae) contain the green pigment and the enzymes that function in the photosynthesis.

The cytoskeleton
All the organelles are not just floating around in the cytosol soup. They are held in place by a network of fibers that runs throughout the cell. These fibers help give mechanical support to the cell. They make up the cytoskeleton.

The cell surface
Cell Walls

Plants have them, animals don't (some fungi, protists and prokaryotes also have walls). Protects the plant, maintains shape, keeps out water. Made of cellulose embedded in a matrix of other polysaccharides and proteins.

The glycocalyx is the protective coating on animal cells that glues one cell to another. Its specific molecules also help cells recognize each other.

These are areas of direct contact between cells. Very important to plants allowing water and small solutes to pass from cell to cell.