Or, are you celebratory of the decision?  In any event, people often inquire what can one person do about such large matters? I offer a sixty word summary first and then in 1051 words I explore more deeply.  My perspective is one of chagrin at the Constitutional compromise that the decision represents.  Perhaps your view is different.  In any case, these suggestions may apply to any viewpoint.

Sixty word summary:

What can one person do?  Be informed. Write a Letter to the Supreme Court. Write a letter to an elected official.  Begin a petition. Participate in or file an amicus brief (assuming the court would be willing to overturn their own decision). Educate yourself on the motivations and rationale of individuals and organizations whose views are counter to your own.
And now for more than 1051 words exploring possible actions for a citizen who has an opinion to express:

What can one person do?  Be informed. Write a Letter to the Supreme Court. Write a letter to an elected official.  Begin a petition. Participate in or file an amicus brief (assuming the court would be willing to overturn their own decision). Educate yourself on the motivations and rationale of individuals and organizations whose views are counter to your own.
IF you have a strong opinion about the Supreme Court’s decision regarding Hobby Lobby, you can do more than type in all CAPS in social media.  I want to encourage you to do one or more of these things.  What better time to exercise your right to engage your legal process and your elected officials than on and around Independence Day.  And, if you would care to join me in a holiday ritual I hold dear, get a copy of the CONSTITION and read it through on the 4th of July.  A lot of lives have been invested and sacrificed to uphold that document.
“THIS REALLY ISN’T ABOUT THAT.”  My view is that the Hobby Lobby case simply serves as the whipping post for folks who are operating with many other items on their agenda.  Considering more than headlines reveals this as a multi-layered, complex issue that has so many motivations behind it it makes my head spin.  At the heart of this, people who oppose abortion and a woman’s right to utilize birth control, and those who want to undermine the continued success of the Affordable Care Act, want to seize this as a current case celebre. That essentially that many folks are simply using the Hobby Lobby case to further their own personal agenda.    And, of course, there are those who earnestly feel from their core that this was a correct decision.  Here again, I would urge a beginning to end reading of the Constitution.
RATHER THAN JOIN THE FIRESTORM OF RAISED VOICES EXPRESSING OUTRAGE, I AM OFFERING AN ADDITIONAL COURSE OF ACTION TO WRITING IN ALL CAPS IN SOCIAL MEDIA.  If you feel strongly consider one or more of these actions.
Write a brief letter to a Supreme Court Justice.
Here are the names of the Cheif Justice and Associate Justice’s currently serving on the  Supreme Court:
John G. Roberts (Cheif); and the Associate’s:  Antonin Scalia, Anthony M.Kennedy, Clarence Thomas, Ruth Bader Ginsburg, Stephen G. Breyer, Samuel Anthony Alito, Jr., Sonia Sotomayor, Elena Kagan.
Write the court or a specific Justsice. State your opinion clearly.  IF you want them to reconsider their action, ask specifically for what you would like them to do.
Address your letter,“Dear Chief Justice Roberts:” or Dear Associate Justice (last name)
Mail your letter to:           The Supreme Court of the United States, U.S. Supreme Court Building1 First Street NE,  Washington, DC 20543
Write a letter to your elected officials.  You can find their contact information here:
http://thomas.loc.gov/home/state-legislatures.html

Sign a Petition or Create your own petition to raise awareness and send along,
ultimately, to the Supreme Court.

Sandra Fluke is orchestrating a petition:  http://www.dailykos.com/story/2014/06/30/1310701/-BREAKING-SUPREME-COURT-DECIDES-THAT-CORPORATE-RIGHTS-TRUMP-WOMEN-S-RIGHTS

http://petitions.moveon.org/create_start.html?source=ads.ck.mop.gs.g08.a01

and here is another site to create a petition:

http://www.thepetitionsite.com/create.html?cid=create_google_0514&gclid=CjgKEAjw286dBRDmwbLi8KP71GQSJAAOk4sjpMczv2lILZVk-Yj2p1dWKGXKSvmcB-nhZrookH7bM_D_BwE

LEARN MORE about the people serving on the court. Here is where you can read a brief biographical bit about the Justices that serve in the highest court in the land:   http://www.supremecourt.gov/about/biographies.aspx
88 Senators and representatives signed an Amicus brief* in Support of the Court ruling in favor of Hobby Lobby.  Patty Murray*, Washington State Senator, signed an amicus  brief  (with 18 other Senators) Supporting the Government’s position against the Hobby Lobby claim in the Supreme Court.  In January Senator Murray explained in 8 minutes why she wanted the Supreme Court to not rule in favor of Hobby Lobby.   See it here:
http://www.murray.senate.gov/public/index.cfm/2014/1/hobby-lobby-murray-leads-senate-democrats-amicus-brief-in-scotus-case
Consider Filing a Legal Opinion known as an Amicus Brief.
An Amicus is essentially a legally recognized statement of opinion. Find out who in your region might be filing an Amicus brief (called Amicus curiae brief)and find how you can participate, or if your interest and resources allow, arrange to file your own.
The Hobby Lobby Ruling may have generated more Amicus briefs than any other court consideration.  I say may because I am unable to substantiate that view.  I have read accounts that say 84 were filed.
Here is a wiki/answer about such a brief:  http://wiki.answers.com/Q/What_are_Amicus_Curiae_briefs_and_who_can_file_them

From Slate. com in an article by Brian Palmer, “Amicus curiae briefs are submissions to the court on behalf of people or organizations that are not parties to the case. It’s difficult to measure their effectiveness because, these days, both sides of most cases receive amicus briefs. At the beginning of the 20th century, amicus briefs were filed in only 10 percent of cases. Amici now participate in 85 percent of high-court cases. Some patterns have emerged, however. Some amici are better than others. The solicitor general, who represents the United States government before the Supreme Court, is by far the most influential amicus a litigant can have before the court. When the administration submits an amicus curiae brief, the government’s side wins 75 percent of the time, and the solicitor general’s winning percentage seems to be increasing. Other experienced organizations, such as the ACLU and the AFL-CIO, are also statistically likely to have their side succeed. If you can’t get a big-shot amicus on your side, hire an experienced attorney. High-profile Supreme Court litigators seem to have more success with amicus briefs than other attorneys do.”

The Anti-Defamation League offers specific viewpoints and in depth information on the workings of the Supreme Court:  http://www.adl.org/supreme-court-review/2014/

The American Center for Liberty and Justice worked hard FOR this decision.  Yes. I said FOR this decision. In case you would like to read about this group of people who worked hard FOR this Supreme Court decision and learn why they think it is a reason for celebration, here:

http://aclj.org/obamacare/in-the-wake-of-hobby-lobby

And here is another organization working diligently to undermine women’s health care in the name of religious liberty:   http://www.becketfund.org/hobbylobbyamicus/

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