By child, if you mean the detail in a master-detail relatio, all you need to do is to create a roll-up summary field on the master (parent.) But if you mean a lookup relation, force.com does not give anything out of the box for that. You can create a count field on parent object and write a trigger on your child object which increments this count field everytime a child record is created (after insert) and decrement everytime a child is deleted(before delete.)
Hi Dev_Sfdc,
I think you have to write a trigger on account for insert,update,delete. Make field on Account first. Child_Count__c
Use following trigger code for you requirement.