The central dogma of molecular biology, a term coined by Sir Francis Crick, states that the flow of genetic information is "DNA to RNA to protein". With the discovery of reverse transcriptase in retroviruses, the central dogma was extended with "RNA to DNA".
It can be stated in a very short and oversimplified manner as "DNA makes RNA makes proteins, which in turn facilitate the previous two steps as well as the replication of DNA", or simply "DNA->DNA->RNA->Protein". This process is therefore broken down into 3 steps: Transcription, Translation, and Replication. By new knowledge of the RNA processing, a fourth step must be included, the splicing.
Transcription is the process by which the information contained in a section of DNA is transferred to a newly assembled piece of mRNA. It is facilitated by RNA polymerase and transcription factors.
Eventually, this ripe mRNA finds its way to a ribosome, where it is translated. The ribosome's function is to take individual amino acids of the correct kind and link them in a chain in the right order, based on the sequence of the mRNA. Once the amino acids are linked into the chain, they are released from the ribosome and fold into a new protein. Sometimes this folding process has to be helped along by other proteins, called chaperone proteins.
Finally, back to where we started, a protein called DNA polymerase opens up the DNA and with the help of several other proteins allows the DNA to replicate itself.
The discovery of retroviruses, which transcribe RNA into DNA through the use of a special enzyme called reverse transcriptase has resulted in the modification of the Central Dogma to include an RNA->DNA pathway. Some people even include Protein->Protein as one of the possible pathways due to the discovery of prions.
See also:
Transcription
Splicing
In eukaryote cells the primary transcript (pre-mRNA) is processed. One or more sequences (Introns) are cut out. The mechanism of alternative splicing makes it possible to produce different ripe mRNA molecules, depending on what sequences are treated as Introns and what remain as exons. Translation
Replication