While having a great script and connections to the actors alma mater might be very helpful, the number one answer to this question is $$$$. Any name actor is going to have an agent or a manager and you or your casting director will have to go thru them. Depending on what the SAG (and you'll almost certainly have to go with a SAG contract if your looking for any kind of name actor) agreement you've signed states scale is, will often decide if an actor even reads your script.
Many agents and managers don't pay attention at all unless the film meets certain budget and financing requirements. Every actor is different and there are some fantastic known actors who read scripts and who want to do indie projects and there are others who won't even look at them. You have to make your wish wish list with your production team and go down your list making offers. Oh yea, most known actors are going to be offer only, which means they won't even consider your project without a written offer.