Make sure you know which citation style your professor wants you to use. You could be asked to use APA, Chicago or MLA style and the formats for each are different.
Locate the passage from which you wish to cite. Gather the name of the pope, the title of the encyclical and the publication date. For in-text citations be able to state the paragraph or section from which you have cited.
Arrange your citation information in the prescribed order dictated by the citation style you have been asked to use.
For example a proper APA style citation would be arranged as: John Paul II. Encyclical Letter. Evangelium vitae. 25 Mar. 1995. 7 Dec. 2007. The in-text citation would look like this: (John Paul II, Evangelium vitae, par. 2).
An example of a correct Chicago style citation of an encyclical would look like this: 55. John Paul II, Evangelium vitae, Encyclical letter on the value and inviolability of human life, Vatican Web site, March 25, 1995, http://www.vatican.va/edocs/ENG0141/_INDEX.HTM, sec. 97. Note that Chicago styles uses footnotes. The proper Chicago style bibliography listing would like like this: John Paul II. Evangelium Vitae. Encyclical letter on the value and inviolability of human life. Vatican Web site. March 25, 1995. http://www.vatican.va/edocs/ENG0141/_INDEX.HTM.
Finally, an example of a proper MLA style citation: John Paul II. Encyclical Letter, Evangelium Vitae: On the Value and Inviolability of Human Life. Washington: United States Catholic Conference, 1995. This is how your in-text citation should look: (Evangelium Vitae par. 4)