Memorize the Tengwar alphabet, which Tolkien's characters use to write various Elvish languages. You can find this alphabet in Appendix E of "The Lord of the Rings" or online.
Practice Quenya pronunciation. Tolkien provides a detailed guide to Quenya phonology in many of his linguistic papers, but because access to these works is restricted, use the somewhat sparse pronunciation guidelines available in Appendix E of the "The Lord of the Rings."
Learn the basics of Quenya grammar. These include the definite article, the formation of plurals, the use of cases, the types and varieties of pronouns and adjectives and verb conjugation.
Read some of the short poems and fragments available in Quenya. In addition to composing original works in Quenya, Tolkien translated many well-known texts into the language, including "The Lord's Prayer" and "Ave Maria."
Tackle "Namárië," the song Galadriel sings during the "Farewell to Lorien" chapter of "The Fellowship of the Ring." "Namárië" is the longest extant Quenya text in "The Lord of the Rings." You can listen to Tolkien chant it in a recording available online.