How do you know if you can claim tax exemption?

Answer 1

If you're asking about claiming an exemption for a dependent, the rules are outlined in IRS Publication 17, chapter 3, and in the 1040 instructions on page 19 and 20. I personally think the table in pub 17 is easier to understand.

These can be downloaded at irs.gov

If your question is about claiming exempt on your W-4. the rules are in the W-4 instructions that are on the form - basically you didn't have any tax liability the previous year and don't expect to have any in the current year either.