I work for a pharmacy delivering meds to nursing homes, there are no taxes deducted from my pay check because the company is exempt from taxes. How should I report my earnings to the IRS?

The company's tax status has no bearing on how you file your Federal return. You still need to report the total that they paid you on your tax return. They should have given you a w-2 or 1099 in January to show how much they paid you. If they did not, then you need to report what they paid you on line 7 of the 1040:
http://www.irs.gov/pub/irs-pdf/f1040.pdf

Or if you can use the EZ form, report your income on line 1:
http://www.irs.gov/pub/irs-pdf/f1040.pdf

If the company is not deducting any taxes from your pay check, it means they are treating you as an independent contractor. They must issue you 1099-misc. You are responsible for paying your own taxes. Your U.S. Tax Return: Tax Filing by Self Employed Sole Proprietor or Independent Contractor

Before you do ANYTHING, go to your employer and ASK if they are going to issue you a Form W-2 or Form 1099. It is possible that your Form W-2 or 1099-MISC just got lost in the mail.

What RickJ says is accurate. Even tax-exempt organizations have to pay FICA (Social Security and Medicare) taxes and withhold federal and state income taxes if they employ someone as an employee.

If they remain evasive (and you do not particularly care about keeping your job), you CAN do what RickJ suggests and submit the needed paperwork to pay JUST your half of the FICA taxes. The IRS will take note and come calling on your employer to get the OTHER half of the FICA taxes. While the IRS will keep your identity secret as the source of the information that sicced them on your employer, they will probably figure out WHO turned them in and terminate your position.