There was a time when bullet point lists were frowned upon in certain forms of writing -- especially academic writing. However, the sixth edition of the "Publication Manual of the American Psychological Association" gives instruction on how to format a bullet list in an essay. Using a list in an essay is also known as "seriation." Lists may include simple bullet points or numbered items, depending on the items to be included in the list.
Finish a paragraph or insert a colon, then move down a space and begin the list. Use numbers, with each number followed by a period, if writing a step-by-step guide or if the order matters. If the list does not require a specific order, bullet points should be fine.
List items should be indented one "tab" -- several spaces -- from the margin and away from the main line of text.
Write each item in the list as a sentence with proper punctuation, ending in either a period or semicolon -- if the list item is logically and closely connected to the list item that succeeds it. Conclude the final list item with a period.
Conclude the list and return to the essay. Leave one space after a list before continuing the paragraph. Capitalize the first letter of the first word, as you normally would. If the list ends your paragraph, use one space (or two, if your essay is double spaced) and begin a new paragraph by indenting and capitalizing the first word.
The type of bullet point used is up to the writer, but simple circular or square points are sufficiently clear and easy to follow.