Chad,

My apologies. 

I'm going to assume you're familiar with the basics of trigger creation (where to go to create one, what the various contexts mean etc.)

Your trigger is going to fire whenever a record of a given type is updated/created/deleted/undeleted depending on how you setup the trigger. So, for the sake of explaination i'm going to assume you're writing this trigger on the project object. 

Here's some highly annontated code to help get you started.
 

trigger RollupProjectCountToAccountTrigger on Project__c (after insert) {

	//Salesforce is going to automatically give you a list of incoming project__c records in a variable called 
	//Trigger.new . Because we're running this trigger *after* insert you also have access to the Trigger.NewMap variable
	//which is a Map record type of <id,Project__c> -- because it uses ID's as the keys, the newMap variable is only avialable 
	//after insert and during update calls when the system has assigned the id.

	// lets kick this off by creating a list of id's that we can use to store account id's. 
	List<Id> AccountIds = new List<Id>();

	// now we'll populate that list with account id's
	// Why? because we're actually going to need those account id's here in just a second.
	// The trigger.new list is only going to contain the *new* project records. our rollup
	// needs to know all of them.
	for(Project__c p: Trigger.new) {
	  AccountIds.add(p.account__c); //this assumes your project__c lookup field to account is called Account__c
	}

	// Now we'll make a query, to get all the project records who's accountID is in the list of new project records.
	AggregateResult[] groupedResults = [SELECT count(id)projectCount, Account__c FROM Project__c WHERE Account__c in :AccountIds GROUP BY account__c]; 
	
	// Additionally, we'll need a group of account objects to update once we've gotten the counts. For this we'll use a map. 
	Map<id,Account> accountMap = new Map<Id,Account>([SELECT id, count_of_projects__c FROM Account WHERE Id in :AccountIds]);

	//Now that we have an account map, we can iterate over the grouped results, and set the account map's data to match. 
	for(AggregateResult ar: groupedResults) {
	  accountMap.get(ar.get('Account__c')).count_of_projects__c = ar.get('projectCount');
	}

	// Lastly, we'll need to update our account objects:
	try {
	  update accountMap.values();
	} catch(DmlException e) {
	  System.debug(e.getMessage());
	}

}

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