I recently became a U.S. citizen, and now wish to sponsor my parents for green cards. I have filed the I-130 visa petition, and am waiting for approval. I understand that this whole process will take some time, and a friend of mine told me that family immigrants have to wait until their "Priority Date" comes up on the State Department's "Visa Bulletin." But I checked there, and I don't see any category for immediate relatives. Am I looking in the wrong place?
Your friend is half right. Family members who are in one of the "preference" categories of the U.S. visa (green card) allotment system receive a Priority Date marking their place in line.
But for immediate, not preference relatives, there is no line. An unlimited number of visas is available to immediate relatives each year, and so the waiting list that is represented on the State Department's Visa Bulletin is irrelevant to them. (Immediate relatives include U.S. citizens' parents, spouses, and unmarried children under the age of 21.)
That is not to say that you and your parents won't have to deal with a wait -- but it's a wait that has to do with government processing of their case, rather than a wait for that processing to begin.
Presuming your parents are living overseas, the next steps will involve USCIS approving the case (and sending you an approval notice) then transferring the file to the National Visa Center (NVC); the NVC sending further instructions and requests for fee payments to you and your parents; and ultimately the NVC transferring your case to the U.S. consulate serving your parents place of residence for further processing and a visa interview and approval.
Nolo's book, How to Get a Green Card, provides a complete guide to this process.