Proselytizing

Proselytizing is the practice of attempting to persuade someone to join a group or adopt a belief. It is used primarily to refer to evangelism, but "deconversion" attempts and nonreligious persuasion (to a political party, say) also fit the definition.

Prominent proselytes
Most Christian groups do missionary work, which generally includes proselytism. Groups particularly noted for proselytizing include:
 * Jehovah's Witnesses
 * The Roman Catholic Church
 * Mormons
 * Born-again Christians
 * Jews for Jesus
 * Southern Baptist Convention
 * The Church of Scientology (through "personality tests")

Legality
The First Amendment to the United States Constitution guarantees both freedom of speech and freedom of religion. Proselytism is legal under both of these provisions, but only to the extent that the potential convert's rights are not infringed upon.

Guides to converting atheists
Various atheists have written descriptions of what it would take to convince them to believe in god(s). Religious groups also have created such guides.

From an Atheist perspective:
 * Ebon Musings: The Theist's Guide to Converting Atheists
 * Barry's blog: How to convert an atheist
 * Common Sense Atheism: How to Convert Atheists

From a Christian perspective:
 * http://www.wikihow.com/Persuade-an-Atheist-to-Become-Christian