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. A person who lives one religion to join another is normally considered an apostate by their former religion.
Many but not all religions attempt to convert people to their beliefs. Christians are particularly known for missionary work, which generally includes proselytism. Groups particularly noted for proselytizing include:
- Jehovah's Witnesses
- The Roman Catholic Church
- Born-again Christians
- Jews for Jesus
- Southern Baptist Convention
- The Church of Scientology (through "personality tests")
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.
It is illegal to proselytize to Muslims in in Malaysia under the Internal Securities Act.  Similar laws exist in many other Islamic countries.
Libya bans proselytizing to Muslims on security grounds. 
Proselytizing in the Bible
"If your brother, your mother’s son, or your son or daughter, or the wife you cherish, or your friend who is as your own soul, entice you secretly, saying, ‘Let us go and serve other gods’ (whom neither you nor your fathers have known, of the gods of the peoples who are around you, near you or far from you, from one end of the earth to the other end), you shall not yield to him or listen to him; and your eye shall not pity him, nor shall you spare or conceal him. But you shall surely kill him; your hand shall be first against him to put him to death, and afterwards the hand of all the people."
- — Deuteronomy 13:6-9 , emphasis added
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: