Eukaryotic cells:

Good nucleus containing DNA and acting like the "brain of the cell"
Contain organelles and surrounded by cell membrane
Cilia(like tiny little arms) & flagellum(whip like tail) are made of microtubules in a structure of 9 pairs around 2 central tubules{9+2 structure}
They help in "movement" of the cell, they are located at the surface of the cell

Cell membrane:

Squishy, encloses cell contents, monitors what comes in/out of cell selectively permeable

Cytoplasm:

Solution of water and nutrients filling the cell, necessary for organelles

Cytoskeleton:

Protein strands that reinforce the cell present inside cytoplasm

Centrosomes:

Assemble microtubules out of proteins

Endoplasmic reticulum(ER):

Organelles that create series of membranes that carry stuff around the cell
These membranes are made of phospholipid bilayers, the same thing that is in the cell membrane.

Rough ER:

Has ribosomes attached to it
Helps in synthesis , quality control of proteins

Smooth ER:

No attached ribosomes
Contains enzymes that help make lipids
Helps in lipid metabolism
Helps in cell detox
stores ions

Ribosomes:

Float freely in cytoplasm or attached to nuclear membrane(released from there)
Assemble amino acids into polypeptides.
Amino acid chain is send to golgi apparatus through ER(after protein chain is ready for dispatch).

Golgi apparatus:

Folds proteins, packages the and dispatches them
Golgi bodies are layers of the apparatus, they cut proteins into hormones and combines proteins and carbohydrates to make various molecules
Vesicles have phospholipid membranes and "ship them" to parts of the cell or outside it.

Lysosomes:

Help in cell digestion and are sacks full of enzymes breaking cellular waste and debris from outside the cell into cell building materials and transferred into the cytoplasm

Nucleus:

Contains "special" type of cytoplasm called nucleoplasm.
Double membrane layer separating it.
It stores the cells DNA and uses it to build proteins for specific actions
DNA stored in web like structure called chromatin, which gathers into rod like structures called chromosomes during cell division

Nucleolus:

No membrane, inside the nucleus , makes rRNA which make ribosome units when combined with some proteins.
These units are released from the nuclear membrane and submerged into ribosomes.
Ribosomes are "told" what to do by some mRNA released from the nucleus
mRNA is messenger RNA , rRNA is ribosomal RNA

Mitochondria:

The power house of the cell
Smooth, oblong organelles.
Respiration takes place here.
Energy is derived from carbohydrates, lipids etc. and turned in to adenosine triphosphate(ATP)
They contain some DNA of their own and used to be separate bacterial cells until they ended up inside of a eukaryotic cell.
Mixes separately during reproduction and we only inherit maternal mitochondrial DNA(99.98% of the time)

Movement of stuff through cell membranes:

Active transport:

Requires ATP , useful for moving stuff against the concentration gradient
When cell needs active transport it gives ATP to a transport protein

Sodium-potassium pump:

In most cells, very important to muscle and brain cells
Work against concentration and electro-chemical gradient
Pumps 3 positive sodium ions into sodium rich outside using energy from bond cleavage of 1 ATP , changing its shape{opens outwards}, it also lets in 2 potassium ions

Vesicular transport:

Vesicles are tiny sacks of phospholipids (similar to cell membrane).That help move substances into/within/out of a cell also called cytosis.
To outside the cell is exocytosis, from outside to inside is called endocytosis.
Exocytosis is used to release neurotransmitters, the vesicle fuses with the cell membrane after reaching it and releases the transmitters .

There are 3 types of endocytosis:

Phagocytosis:

Reach out around the outside substance, engulfing it and form a vesicle to take it inside.
White blood cells use this to kill invaders

Pinocytosis:

Membrane folds a little to surround dissolved substance and form a vesicle to hold the fluid
Cells absorb nutrients in this manner

Receptor mediated endocytosis:

Use clusters of specialised receptor proteins in membrane which form vesicles when the receptors connect with the molecule they are "looking for"
Used for molecules with very low concentrations, like cholesterol

Passive transport:

Doesn't require energy, used in intake of water and oxygen via diffusion

Channel proteins:

Allow passage of water and ions without energy
They straddle the width of the membrane and have hydrophilic channels inside
Proteins for channelling water are called aquaporins {up to 3*10^9 water molecules!}

Hypertonic: concentration of solution inside cell is higher than solution outside cell
Hypotonic: concentration of solution inside cell is lower than solution outside cell
Isotonic: concentration inside and outside is same