The Church of Satan does not solicit membership. Those who wish to affiliate can become Registered Members for a one-time registration fee of two hundred dollars ($200) in United States currency.

Taken from the Church of Satan's official website:

Registered Membership

We don't solicit memberships; however, if you wish to join us to show your support or appreciation you can become a Registered Member. For a one-time registration fee of two hundred dollars in United States currency, you will receive an embossed crimson card declaring you a member of the Church of Satan. This card is your means for identifying yourself as a genuine member of the Church of Satan to other members. If you expect to meet another member for the first time, be prepared to produce your card.

No further dues will be expected. There are no further obligations. You must be legally an adult in your nation of residence.

It is not humankind's job to 'save' anyone. Only God saves.

A repentant and baptized Christian, begotten by the Spirit of God, is to lead a life doing God's good works which He has established for them from the beginning (see Ephesians 2:10 and others). A Christian is to be an 'imitator' or disciple of Jesus which by this perfect example will draw others to seek the who, what, why and how. By their lives examples, the curiosity of others will spike perhaps leading them to the Scripture in search of knowledge and wisdom.

What we must always remember though is that only God calls each of us to His Son at the best time for us by His Will. No human can bring someone to Christ:
John 6:44

No one can come to Meunless the Father who sent Me draws him; and I will raise him up at the last day.

John 6:65

And He said, “Therefore I have said to you that noone can come to Me unless it has been granted to him by My Father.”

Answer from a Satanist

For the most part, we feel that it was the name that was put on us.

For example, we believe in breaking all of "the 7 deadly sins" as it leads to physical, mental and emotional gratification. In previous years, the Church would have had us tortured and killed for being Devil worshippers because of the philosophies we believe in and live by.

Also, it's no secret that some Satanist perform Black masses, which again in previous years would have earned us the title (as well as an early death) of a devil worshipper, disciple of evil or a Satanist. Now that times have changed, and the Church can no longer kill us or torture us we kept up the title.

Lastly, LaVey went into some detail (which I'm not going to get into here) about how 'Satan' means the adversary. Since we oppose a lot of the Christian dogma it was a suitable title.

Satanism is, in a sense, a genre of different religions put together. Some people consider Pagans, Occultists, Wiccans, Luciferians, and Atheists to be under this category.

Answer from a Luciferian

Satanism is a very broad description. Satanism includes Luciferianism, LaVeyanism, Occultism, and several others. Satanists were considered satanists because we are considered adversaries of the Christian church.

Many LaVeyans are atheists, while all Luciferians believe in God and Lucifer (Satan). Luciferians worship Lucifer as a good deity. This is where the name came in, since Lucifer (after his fall from heaven) became Satan.

Answer from a Theistic Satanist

Our beliefs vary but we all agree that Satan is the deity we worship what differs is our belief about that deity. whichever way Satan is what we call who we worship and the reasons vary as one must get to know Satan personally.

Answer from an outsider

The name Satan simply means adversary. LaVeyan Satanists are mostly atheists and thus consider themselves adversaries to organized religion. Theistic Satanists call themselves Satanists since they worship the deity who was maligned with the name Satan and who, by nature, opposes the god of the Bible.

Answer

Very discreetly and never under the name of "Satanism". Look up Temple of Set, there's one branch of Satanists. They acclaim themselves with great "intellect" and insight into things.

Answer

Then there's The Order of Nine Angels. They recruit based on how discreetly one can murder another person. Apparently, the founder switched to Islam, but from one with such strict beliefs, it is actually doubted what the founder's true activities are.

Although, it should be assumed that religions don't recruit people, rather people choose their religion. At least, that would be the preferred method of finding yourself in a religion.