It can take 6-8 weeks from the time the decision was made for benefits to be sent out. You will first get your backpay check (if any) that will show up either BEFORE your award letter (which is different then the approval letter, the award letter lays out what your benefits are, what was withheld for the attorney etc) or shortly afterwards (depending on if you have direct deposit or not). The award letter will tell you when your monthly benefit starts (you will get paid on a Wed. depending on what part of the month your b-day is in) So if you have a late month b-day, you will get you payment at the end of the month.
SSA ALWAYS pays a month behind. So if your payment date is the last Wed of the month and its June, you will receive your MAY payment on the 30th of June this year.
Also, if you have children, remember to apply for their benefits as well!