I'm Lucy, and I'd be happy to answer your questions today.
The crime of conspiracy is complete when two or more people agree to commit any crime, with the intent that the crime be committed. Cal. Pen. Code, Section 182. It's also a conspiracy to agree with someone else to falsely accuse someone else of a crime, file a false lawsuit, cheat someone out of property, or obstruct justice. The crime is in the agreement. However, the indictment or information must allege that one or more acts was taken by some member of the conspiracy to complete the crime. Additionally, any person who is a member of a gang and benefits by criminal conduct of other gang members is considered to have conspired with them under Cal. Pen. Code, Section 182.5.
It is possible for a warrant to be issued without a person ever being charged. That sometimes happen when police can't find a person, but it can also happen if they mailed you notice of a court date and you didn't show up. Notices frequently go to the address on your driver's license - the most common way that people get a warrant is that they didn't receive a notice because they didn't update the DMV when you moved. That's not the only way, but it's pretty common.
You have a right to know what the charges against you are. If you've been taken into custody, they will take you before a judge, who will explain exactly what you are accused of doing. Not just a conspiracy, but the specific offense. You have a constitutional right to ask for a lawyer to represent you if you cannot afford one. The judge must appoint one for you if the crime is one that can be punished by jail (whether jail is ultimately likely or not).