How do you find what someone owes in back income tax?

If "someone" is you or if you have a legal power of attorney or guardianship or conservatorship over "someone," then you can call the IRS and ask. Of course, the IRS can only tell you about taxes that have been assessed. If "someone" has failed to file tax returns or been concealing income, the IRS might not have that information. You can also contact the state and local tax authorities to get information about state and local taxes.

If "someone" is not you, then you ask "someone" if they will tell you. If "someone" asked for your help, you can help them contact the IRS and get the information.

If "someone" doesn't want to share this information with you, there is little you can do. If you are in some situation where you might have a legal need to see this information, you can try to get a court order to compel "someone" to produce their records. You should probably consult with a lawyer about this.