First, don’t worry. None of the characters print.
The dots and arrows certainly are a nuisance, but those strange ¶ symbols are really your friends. They show exactly where each paragraph ends. Since all paragraph formatting (tabs, indents, margins, line spacing, before and after paragraph spacing, ...) is attached to them, accidentally deleting one can cause mysterious reformatting problems. I've found it's nice to know where they are.
If you still want to get rid of everything, do this:
In versions of Word prior to Word 2007:
1. Click the ¶ button on the Standard toolbar.
In Word 2007:
1. Click the ¶ button in the Paragraph section of the Home tab.
But if you want to turn off just the other characters, here's how:
In Word versions prior to Word 2007:
1. Click the Tools->Options menu item.
2. Click the View tab.
3. Under Formatting Marks, select ONLY Paragraph Marks and deselect all others.
4. Click OK.
In Word 2007, do this:
1. Click the round Office button in the upper-left corner of the window.
2. Click the Word Options button.
3. On the left side of the dialog box, click Display.
4. Under Always Show These Formatting Marks On The Screen, put a check mark next to Paragraph Marks.
5. Make sure all the other entries in this section are unchecked.
6. Click OK.
That's it.