A paragraph is a group of sentences that develop the same idea and show a unity of thought. Organizing your ideas into paragraphs helps you to organize your thoughts and if your ideas as organized, your reader will understand you better.

From a layout point of view,  paragraphs can be indented or written in block style but they tend to be separated (single or double spaced) from each to signal the start of a new idea and give the reader a break between one idea and the next.

There are no rules as to how long a paragraph should be.  It will need as many sentences as necessary to develop an idea.  If your paragraph has only one sentence you should ask yourself if you have developed an idea to the full.  On the contrary, if your paragraph is too long, it is time for you to consider if some of the ideas in your paragraph could well be the subject of another paragraph.

A well-written piece of writing shows paragraphs of about the same length.  That shows you have taken your time to organize and give the same length.  Usually the introduction and the conclusion tend to be shorter that the paragraphs in the development section but it is always subject to the length of the task.  Sometimes if background details have to be given or if conclusions have to be drawn the introduction and the conclusion could expand over two paragraphs.

Paragraphs tend to open with a topic sentence.  This sentence should be a summary of what is going to be developed in the rest of the paragraph and relates to thesis the writer is trying to make.  The topic sentence tends to appear at the beginning of a paragraph, and it is usually the first of the second sentence in that paragraph.

The topic sentence is then developed by using descriptions, classifications, analysis, comparisons and cause and effect.  At the end of the paragraph there is always a conclusion that reformulates the point made throughout the paragraph.  There are times when the conclusion marks the transition towards a new point that will start in a different paragraph.  However, the conclusion should not introduce an idea that has not been developed in the paragraph. That idea should be in a new paragraph.

Every paragraph has an introduction-development-conclusion structure that is signaled by a topic sentence, its development and a conclusion. 

Paragraph Builder http://www2.actden.com/writ_den/tips/paragrap/index.htm

Royal Literary Fund:

http://www.rlf.org.uk/fellowshipscheme/writing/planningandstructure/ParagraphsLinks.cfm

Academic Phrasebank: http://www.phrasebank.manchester.ac.uk/introductions.htm