More to the point, the time varies. First, they have to contact you, usually by phone. Then, they have five days to send you a letter which will tell you that you owe someone some money and to send it to the address they've provided.
However, also in that will be a notification that if you dispute, or ask for validation of the debt, and/or the name and address of the original creditor, all collection efforts are suspended. You have 30 days to send a letter to them. Once they receive it, they either have to send you the information or leave you alone.
If they do send you PROPER validation, then they can sue. The time this will take varies from CA to CA. For example, if a debtor is sued by Hanna and Associates, out of GA, he can expect to be sued within three months or so. Others may not get it going for many months, even a year is not that unusual.
The important thing is to respond to their summons. Through discovery, make sure to demand every iota of proof. Much of their "proof" will be hearsay and mostly incomplete, and sometimes bogus. It is up to the debtor to challenge and question each step of the way.
The CA is counting on most people, as much as 90%, not to show up at the court. Don't be one of those people. Show up, make them know they're in for a fight, and don't be suprized if the CA will dismiss his efforts on the spot; or at worst, ask for a continuance, since it is a sure bet the CA's attorney will be ill-prepared. When that happens, it becomes that more costly for the CA to continue chasing windmills.
Becoming educated to the process is a winning strategy when dealing with collection agencies. Check out some very good research sources like debtorboard.com and creditinfocenter.com.