Illinois and Wisconsin have a reciprocal agreement.
That means you only pay tax to the state in which you live.
If you are in Wisconsin ONLY to attend school, you may still be considered a resident of Illinois.
If you are a dependent, and the person that claims you is an Illinois resident, you are an Illinois resident as well.
Obviously you would report both W-2 forms in the federal section.
You don't enter your W-2 a second time.
Next you would file an NON-RESIDENT Wisconsin state return to get the tax withheld back.
Allocate none of your income to Wisconsin.
You may be charged local tax, such as city or county if you worked in an area with local tax. That is no-refundable.
Finally file the RESIDENT Illinois return. You will be taxed on your full income. You most likely will owe tax to Illinois since Illinois tax was not withheld by your Wisconsin employer. Your Wisconsin refund cannot be sent to pay your Illinois tax.
Lastly, Illinois tax my be LARGER than Wisconsin tax, so your Wisconsin refund may be less that the tax due to Illinois.
Reciprocal state info
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