I'm learning UNIX on my mac (BSD), using a manual. I'm trying to figure out the grep command, and am getting something wrong. I've opened one of my files in NeoOffice and am looking for a string, the phrase 'I am writing.' I've been to some sites to get the proper syntax, and from what I can see the proper syntax is:

grep "I am writing" [file name]

A lot of times I get the message that no such file or directory exists, even when I think I've entered all the information. When that doesn't happen, the cursor just blinks, with no display of the string I'm looking for. Can someone tell me what I'm missing? Granted, the book i'm using is the OS X missing manual by david pogue, and it's only a few paragraphs on the command, so I may not be comprehending something. Please, if you could write out the proper syntax (including any slashes, dots, etc.) so I can compare it to what I'm doing.

grep will return all lines that contain a searched-for string.
And I have seen some odd results when the lines are not delimited as usually expected with a line-feed at the end of each. So, that is a first thought - that your file is not correctly delimited. (see commands like dos2unix and unix2dos for more on this)
The next issues are capitalization and spacing. The grep command, without additional options, is an exact match. This relates to my comment on spacing as there might be two spaces between certain words, they words may be on separate lines, there could be tab characters between the words.

See the following example:

Can you explain what you mean by 'delimited?'

I just copied the NeoOffice file (saved as .doc, a word format) to text edit (a .txt file) and the command worked (grep 'I am writing') but it printed the whole letter, or most of it -- which I'm guessing means that it found all the lines with any of the three words in the string and printed those lines. Is it possible to use 'grep' to find this particular sentence fragment and no other lines which don't contain this entire fragment?

Copying a .doc to something named .txt does NOT make it a text file.

I think this is the basis of your problem and misunderstanding.

Try doing a "Save As" and choose something that is Text (I don't know what Neo offers you, probably "Text", perhaps some variants).

Grep is designed to work on text files, not wordprocessor files.

I saved it as a txt file (text) in NeoOffice. But the grep command doesn't work. I entered grep "I am writing" then the pathname, ending with the file name (\name\ name\ name\.txt [The file name consists of three letters, with a space between them, no space between the last word and dot) but got the message 'No such file or directory.' when I try it with the copy saved in Apple's Text Edit (the txt extension) application it worked fine.

Can you tell me exactly what is meant by a text file and how it differs from a word processing file? Because I can choose fonts and formatting in Text Edit, just like Word or NeoOffice.

Put the filename with spaces in it inside speech marks, e.g.:
File names with spaces are best avoided for Unix...