Please help me fill out this information on the Landmark case of Sherbert vs. Verner.

You need to work on research skills. It only took me a few moments to find:
Here is a summary of the case:
[quote]Sherbert v. Verner, 374 U.S. 398 (1963)
Syllabus

Appellant, a member of the Seventh-Day Adventist Church, was discharged by her South Carolina employer because she would not work on Saturday, the Sabbath Day of her faith. She was unable to obtain other employment because she would not work on Saturday, and she filed a claim for unemployment compensation benefits under the South Carolina Unemployment Compensation Act, which provides that a claimant is ineligible for benefits if he has failed, without good cause, to accept available suitable work when offered him. The State Commission denied appellant's application on the ground that she would not accept suitable work when offered, and its action was sustained by the State Supreme Court.

Held: As so applied, the South Carolina statute abridged appellant's right to the free exercise of her religion, in violation of the First Amendment, made applicable to the states by the Fourteenth Amendment. Pp. 374 U. S. 399-410.

(a) Disqualification of appellant for unemployment compensation benefits, solely because of her refusal to accept employment in which she would have to work on Saturday contrary to her religious belief, imposes an unconstitutional burden on the free exercise of her religion. Pp. 374 U. S. 403-406.

(b) There is no compelling state interest enforced in the eligibility provisions of the South Carolina statute which justifies the substantial infringement of appellant's right to religious freedom under the First Amendment. Pp. 374 U. S. 406-409.

(c) This decision does not foster the "establishment" of the Seventh-Day Adventist religion in South Carolina contrary to the First Amendment. Pp. 374 U. S. 409-410.

240 S.C. 286, 125 S.E.2d 737, reversed.
[/quote]
This was a U.S. Supreme Court case, an appeal from South Carolina (probably state supreme court) which it reversed.
Adele Sherbert was the Plaintiff -see above. Verner was chairman of the Unemployment Commission.
However, the case no longer appears to be "good law" in its breadth of holding. But that is a complicated topic.

https://en.m.wikipedia.org/wiki/Sherbert_v._Verner

Looks like bad law to me at first glance, but dm me if you really need help and I'll read the case

1. Adell Sherbet, who was fired for refusing to work on the Sabbath.
2. Charlie Verner, the chair of the South Carolina Employment Security Commission, who denied her claim of wrongful termination.
3. The Supreme Court, in a 7–2 decision, reversed the Commission and the lower courts and found that as applied, the government's denial of Sherbert's claim was an unconstitutional burden on the free exercise of her religion. The majority opinion effectively created the Sherbert Test, determining whether government action runs afoul of the Free Exercise Clause.

Now, this is the last time I'm going to do your homework for you. You can Google your own homework, lol.