For this election only, the Democrats in the Illinois General Assembly have passed a law to allow people to register on Election Day and, thereafter, vote.
Here is what McHenry County Clerk Kathie Schultz has to say about the process:
A voter must have 2 forms of ID, both with current name and one with current address.
They register and vote at that time.
This can only be done at
my [Woodstock] office
the City of Crystal Lake
the City of McHenry and
the Village of Lake in the Hills