What is the correct way to use "neither" and "nor" in a sentence together?

The neither/nor combination expresses negation all by itself. Therefore it should be used with a positive statement. The following is correct.

I can find the tool neither in the kitchen nor in the bathroom.

Or for simplicity you could just leave out the neither/either

I can't find the tool in the kitchen or the bathroom

is perfectly understandable.

This also has the advantage of working when talking to computer programmers who would look confused if you had searched for a single tool in the kitchen AND the bathroom.

You need to either use a negative verb ("cannot"), or use neither/nor. Using the two together, like what that editor did to your post in TeX, is incorrect.

I can find the tool neither in the kitchen nor the bathroom.

I can't find the tool either in the kitchen or the bathroom.

I can't find the tool neither in the kitchen nor the bathroom.

I do want to note that, unless the context leads the reader to expect a negative, the "can find ... neither" version can be confusing. Thus, "can't find ... either" is in most cases the better choice.

I know this has been answered, but I couldn't resist chiming in anyway.

Think of it this way:

• Neither = not either
• Nor = Not or

I cannot find the tool not either in the kitchen not or in the bathroom.

Cannot + not = Can => I can => not what you're trying to express