It's really simple! Organisms that have been scientifically described have two names*, a genus name and a species name. The first one is the genus name. It always begins with an upper case letter. The second is the species name. It never has an upper case letter.
For an example, I give you Heterodontus portusjacksoni, better known as the Port Jackson Shark. The whole name is written in lower case letters except the first letter of the genus name. Both names are written in italics. Simple! If you are hand-writing the name and italics cannot be used, underline both words, Heterodontus portusjacksoni.
The genus and species names are usually derived from Latin or Greek but often include a person's name. The genus name Heterodontus comes from the Greek heteros meaning 'different' and dont meaning 'tooth' This refers to the difference between the anterior teeth which are small and pointed and the posterior teeth which are broad and flat. The species name portusjacksoni refers to Port Jackson, better known as Sydney Harbour.
Phew. I feel better now!
*I am ignoring subspecies, races, vars etc.