This is a multi-step process. Each one of these documents will require individual attention and trips to various offices. But it can be done.
Before going into specifics, it is important to know where to go. Tel Aviv or Jerusalem: There are three US government offices in Israel which will be able to help you with processing your forms: the embassy in Tel Aviv, the consulate in Jerusalem and the consulate in Haifa. Be sure to go to the correct office. If you live in Jerusalem or in Judea/Samaria, then you must go to Jerusalem. Everyone else can go to Tel Aviv or Haifa (most go to Tel Aviv). If you make appointments at the wrong office you will be turned away.
Also, when going to the US embassy or consulate in Israel, be sure to read up ahead of time on what you can and cannot bring (hint: they don't let you bring your phone inside). If in doubt, don't bring it.
Israel Birth Certificate & Passport
First get your Israeli documents in order. You will get a document from the hospital giving you details on the child's birth. Don't lose this. Take this to the closest Israeli Ministry of Interior office (Misrad haPnim) soon after the birth in order to get an Israeli Birth Certificate. (Their website is only in Hebrew and Arabic, but you there is a list of offices in English here). This is a pretty easy process (go with both parents and the kid, show them your Identification and the form from the hospital, tell them the name) at the end of which you will receive an Israeli Birth Certificate. Important: be sure to give them the child's English with its proper spelling, and ask them to print the birth certificate with the English translation (they can do this very easily but wont unless you ask). You must have this English translation to proceed.
While you are going to the Interior Ministry office, also apply for and get a passport for the baby (take passport photos ahead of time). They can do it all at one time, and it is good to have the Israeli passport on hand for your visit to the US government offices.
US Birth Certificate / Consulate Report of Birth Abroad
Now make an appointment for getting your Consular Report of Birth Abroad (sorry, you won't be getting a US Birth Certificate. Instead you get a CRBA, which is basically the same thing). Go to the embassy or consulate website to make an appointment (you might need to do this a few weeks in advance). Be sure to read the requirements on the website for the exact documentation that you will need to bring and be organized ahead of time. In addition to the child's Israeli birth certificate and passport, and the parent's identification, you may also need to bring documentation of the parent's US citizenship, proof of physical presence and more. If you have questions, contact the office ahead of time to avoid wasting time. And fill out the application ahead of time.
As of now, the embassy website permits you to apply for a Social Security Number at the same time that you get your CRBA. So fill out the form ahead of time and bring it with you.
Note: the rules on this change from time to time, so check up on what you need to do. In the past, you were not allowed to apply for your SSN until after you received your CRBA.
When you go for your CRBA, take the opportunity to also apply for a US passport for the child. The documentation that you need in order to do this greatly overlaps with what you need for the CRBA, but double-check ahead of time to be sure that you have everything. Be sure to get US size passport photos (different than Israel size) and fill out the form ahead of time.
Good Luck. When you go to the embassy or consulate, get their with plenty of time to spare for parking, traffic or anything else, triple check that you have all that you need, and try to stay calm. With good planning and a little bit of luck (and your credit card), you should be able to submit all of your applications in one trip, and will hopefully receive the documentation in the mail within a month or two.