It would be rather inefficient to manually count words .
The first step to word count is by choosing a text editor

notepad - txt format
wordpad -rtf format
MS word -doc format
Other freeware/sharewares.

Notepad and Wordpad do not have a word count/character count facility.
So although you are able to articulate your ideas well without thinking much of formatting and all the clutter around, you are not able to count the number of words.
The case with MS word is exactly the opposite!
For a Microsoft word count, well simply go to the Tool menu, (do not select anything) and click on word count.
It gives the number of words, characters(no spaces), character(with spaces)
Number of lines/Paragraph/Pages etc.

However, personally, I liked the Textpad from textpad.com for editing over MS word.
Firstly, because I love the tab feature. Secondly, because of the simplicity and ease to work with txt yet have a powerful array of short-cuts and features.The tab feature allows you to jot down multiple ideas coming in your mind in different tabs, thus organizing thoughts and keeping things efficient.

To word count, Simply select the text, right click on 'properties'. A tabbed window opens, select the Document tab which shall have the details.
Characters,Words and Lines.

Cheers! happy essay writing!!