What to do with 1042-S withholding tax credit slip you received
If all of your earnings are from treaty zero-rated withholding such as royalties from US publishers:
You should claim a zero rate by providing W-8BEN to all (say, publisher) payers to prevent withholding from occurring at the get-go.
Meanwhile to get back the money they withheld by claiming it back as refund by filing a tax return.
Check that preparer fee versus refund will be cost beneficial.
If you earning other US source income that is subject to withholding:
See if that income is exempt from withholding, or if a reduced tax rate applies, under treaty
Compare the amount withheld to the amount owed in withholding
If correct, generally there’s no action to take or required (unless received as rent income from a US property – as more favorable outcomes can be put into place)
If over-withheld, see above for refund claim options.