The most widely used phonetic alphabet, that provides suitable symbols for the sound of any language, is the International Phonetic Alphabet, or IPA. It was first published in 1889 by the International Phonetic Association in France and has since then been revised and corrected in various ways, most recently in 2005. It is a system of phonetic notation, which uses a mixture of some symbols from the Latin and Greek alphabets, some symbols used in written Old English, and some that are specially invented.
It is designed to represent those qualities of speech that are distinctive in spoken language: phonemes, intonation, and the separation of words and syllables. As of 2005, there are 107 distinct letters and 56 diacritics (also called an accent, a small sign added to a letter to alter pronunciation or to distinguish between similar words) and suprasegmentals (the prosodic features of a unit of speech) in the IPA proper. Occasionally symbols are added, removed, or modified by the International Phonetic Association.
You can find a very useful printable IPA-chart with sounds and names for all the symbols and much more here: http://www.yorku.ca/earmstro/ipa/
Once you have made yourself familiar with the IPA-symbols, go back to the page phonetic alphabets to check your knowledge.