In addition to folding the stroller and sending it through the x-ray scanner, you will also need to remove the carseat and send that through the scanner as well. You must carry your child through the metal detector with nothing else in your hands except your ID and boarding pass. All toys, blankies, etc. must also pass through the scanner. (You may not carry a baby through in a sling or Bjorn carrier; they will make you take those off and put them through the scanner, too.) TSA agents won't fold or organize any of your equipment for you; you have to do it on your own.
Before getting into the security line, take out your ID and boarding passes and put them in a pocket so that they are on your body. When you first get into the security line, REMOVE any and all objects that are hanging on the stroller or in the basket; all that stuff has to go through the scanner, so you want to put it in a bag before you actually reach the checkpoint. Don't put shoes on your infant, because you would only have to remove them for security: go with socks only, and don't dress the child for travel in overalls with metal hooks/buttons. Also, don't forget that you will have to remove your own shoes, so wear some that you can take off and put on while holding the baby.
For the sake of your own sanity and that of everyone in line with you, it is best to put ONLY your diaper bag on your stroller when you are in the airport, and easiest to hang it on the handles rather than putting anything in the basket (put your "handbag" stuff in one of the diaper bag pockets instead of carrying a separate purse.) Don't have a pile of loose items in the basket or a lot of toys attached to the napper bar. In fact, it is best to totally remove the napper bar and the stroller hood and put them in a checked bag; it lessens the opportunity for those attachments to get damaged, and it helps the stroller fit through the scanner more easily. If the *folded* stroller will not fit through the scanner, it will be searched by hand. (You must fold it and attempt to put it through, they won't take your word that it is too big, even if you know that it is.) If that happens, you don't push it through; you turn it over to the agent who takes it through, wands and searches it, and then returns it to you on the other side.
If the baby is not flying seated in the carseat, you will have to gate-check that separately from the stroller; you may not leave them hooked together when gate-checked. (You wouldn't want to, anyway: major likelihood of damage if you did.) Again, all add-on gadgets, toys, etc. need to come OFF of the stroller and carseat before it is gate-checked, so it is best just not to have them there at all while transiting the airport. If you want a protective bag for your gate checked carseat, ask for it at the ticket counter; the gates usually don't have any plastic bags available. You must fold and tightly secure the stroller before leaving it at the end of the jetway; if you don't, it will usually be thrown into the hold as is, unfolded, which almost always will result in damage.