There is no requirement that there be a "reading of the will." Therefore, there is no requirement that you be present for one.
How long after a will is read do you receive what was left for you?
It depends upon a number of factors, such as, how complex the estate is. For a probate estate with few complexities, 6 - 12 months is probably a good estimate.
And there is no guarantee that you will receive anything. If the deceased had debts, those debts have to paid first. Only after legitimate creditors are paid do the beneficiaries receive bequests.