Max,

I am new to salesforce but I believe there are several issues here. I am considering you would like to maintain the count of the students of a particular class in a class record.

a. Trigger.New is available only in insert and update triggers. And is updateable in before triggers only.
b. You are updating a field in class__c object in the trigger of Student__c, you would need to do a explicit update here. (atleast that what I read, may there is a cool way other than that I am not sure).
c. Each time in the loop you are doing a query to the get a count of the student records for a given class, which we can avoid as it might be unneccessary if say all the records belong to the same class.
d. In the second if you are checking isAfter and isDelete where as you have registered the trigger as before delete. I think that one must be a typo.

Now, If Class is a master of Student (typically it would be) I would rather add a roll-up field for this. But if I had to do it through a trigger I would do something like this.
(* Note just a sample it can be written in much efficient way)

trigger updateCount on Student__c (after insert, before delete)
{
//////////////////////////////////////
// When insert/update any student’s in class then update MyCount Accordingly.
// Created 20131009 max
// Modified 20131009
//////////////////////////////////////
	Set<Id> sClassIDs = new Set<Id>();
	Map<Id, Decimal> mClassWithCounts = new Map<Id, Decimal>();
	
	List<Class__c> lClassListToUpdate = [select id, My_Count__c from Class__c];
	
	for (Class__c classItem : lClassListToUpdate) {			
			mClassWithCounts.put(classItem.id,classItem.my_count__c );			
	}
	
	if(Trigger.isAfter && Trigger.isInsert)
	{
		for (Student__c stent : Trigger.new)
		{	
			Decimal dCurrentCount ;			
			if(mClassWithCounts.containsKey(stent.Class__c)) 
				dCurrentCount = mClassWithCounts.get(stent.Class__c)+1;
			else 
				dCurrentCount = 1;
			mClassWithCounts.put(stent.Class__c,dCurrentCount);
		}				
	}
	if(Trigger.isBefore && Trigger.isDelete)
	{
		for (Student__c stent : Trigger.old)
		{	
			Decimal dCurrentCount ;			
			if(mClassWithCounts.containsKey(stent.Class__c)) {
				dCurrentCount = mClassWithCounts.get(stent.Class__c)-1;
				
			} else {
				dCurrentCount = 0;			
			}
			
			mClassWithCounts.put(stent.Class__c,dCurrentCount);
		}				
	}
	
	if (mClassWithCounts.size() > 0) {
	
			
		for (Class__c classItem : lClassListToUpdate) {
			system.debug(mClassWithCounts.get(classItem.id)); 
			classItem.my_count__c =  mClassWithCounts.get(classItem.id);
		
		}
		
		update lClassListToUpdate;
	}

}