The cell is the elementary unit of all living organisms. The following picture shows a typical eukaryotic cell.
(Source: Wikipedia)
(1) Nucleolus (dt. Nukleolus)
(2) Nucleus (dt. Zellkern)
(3) Ribosome (dt. Ribosomen)
(4) Vesicle (dt. Vesikel)
(5) Rough endoplasmic reticulum (ER) (dt. Raues Endoplasmatisches Reticulum)
(6) Golgi Apparatus (dt. Golgi-Apparat)
(7) Cytoskeleton (dt. Mikrotubuli)
(8) Smooth Endoplasmic Reticulum (dt. Glattes ER)
(9) Mitochondria (dt. Mitochondrien)
(10) Vacuole (dt. Lysosom)
(11) Cytoplasm (dt. Zytoplasma)
(12) Lysosome (dt. Mikrobodies)
(13) Centrioles within Centrosome (dt. Zentriolen)
(2) Nucleus (dt. Zellkern)
(3) Ribosome (dt. Ribosomen)
(4) Vesicle (dt. Vesikel)
(5) Rough endoplasmic reticulum (ER) (dt. Raues Endoplasmatisches Reticulum)
(6) Golgi Apparatus (dt. Golgi-Apparat)
(7) Cytoskeleton (dt. Mikrotubuli)
(8) Smooth Endoplasmic Reticulum (dt. Glattes ER)
(9) Mitochondria (dt. Mitochondrien)
(10) Vacuole (dt. Lysosom)
(11) Cytoplasm (dt. Zytoplasma)
(12) Lysosome (dt. Mikrobodies)
(13) Centrioles within Centrosome (dt. Zentriolen)
One of the cell's tasks is to produce proteins. Proteins give the cells their structure and they are the molecular machines that transport substances, catalyze chemical reactions, act as messengers and recognize molecular cues (work as receptors). Proteins consist of amino acids. The process of building proteins begins within the nucleus where the DNA is transcribed into mRNA (messenger RNA) and tRNA (transfer RNA). Later, the mRNA and tRNA diffuse out of the nucleus into the cytoplasm. The DNA never leaves the nucleus.
Afterwards, the ribosomes translate mRNA and tRNA into proteins.
(Source: Wikipedia)
A ribosome does this by using the mRNA as blueprint for the protein building process. The tRNA acts as input building block with each tRNA having bound one animo acid. The output of this process is a chain of amino acids, the protein. First, the ribosome reads three nucleic acids from the mRNA. Then the complementary nucleic acids of some matching tRNA are bound to that piece of mRNA. At the same time the amino acid of the tRNA connects to the newly synthesized protein. Afterwards the next three nucleic acids of the mRNA are read and so forth.
If proteins leave the cell after being build to act as messengers or to recognize molecular cues they do this with the help of vesicles and motor proteins. Therefore the vesicles and motor proteins carry the proteins to the cell membrane where they merge with it and free their cargo.
Now e.g. the messenger proteins trigger the building process of proteins within neighboring cells and the whole game starts all over again.
The Harvard College did a great video that visualizes the inner life of a cell.
At 4:31 you see some mRNA leaving the nucleus. At 4:49 and 5:22 a ribosome builds a protein out of mRNA and tRNA. 5:43, 6:17 and 3:43 show how a motor protein transports a vesicle (e.g. containing some proteins and other stuff) to the cell membrane. Later at 6:25 the vesicle and the cell membrane merge and the vesicle frees its cargo. Some of the contained proteins act as messengers and some others act as receptors as it is shown at 6:40.
What impresses me most is the massive concurrency present within each of our body cells. And we have many of them :-) (the human body has approximately 100 000 000 000 000 cells).