• You need to create mapping for Zip/Postal code with Lookup Object i.e. exact same mapping so that Apex would identify the unique record. 
• create trigger on before Insert, Before Update
• Before Insert:
  • Check ZIP / Postal code isn't blank. 
• Before Update:
  • Check ZIP / Postal Code is not same as Old Map i.e. previous value or blank. 

• Trigger Account_AT on Account (before Insert, before Update)
  {
  	List<String> postalCodes = new List<String>();
  	set<id> removedPostalCodes = new set<Id>();
  	for(Account acc : Trigger.new)
  	{
  		if(trigger.isInsert && acc.BillingPostalCode != '')
  			postalCodes.add(acc.BillingPostalCode);
  		else if(trigger.isUpdate && (acc.BillingPostalCode != OldMap.get(acc.id).BillingPostalCode))
  			postalCodes.add(acc.BillingPostalCode);
  		else if(trigger.isUpdate && (acc.BillingPostalCode != OldMap.get(acc.id).BillingPostalCode && acc.BillingPostalCode == ''))
  			removedPostalCodes.add(acc.id);
  	}
  	
  	Map<String, ZipCodeObject__c> zipRecords = new Map<String, ZipCodeObject__c>();
  	for(ZipCodeObject__c zip : [SELECT Id, Name FROM ZipCodeObject__c WHERE Name IN :postalCodes])
  	{
  		zipRecords.put(zip.Name, zip);
  	}
  	
  	for(Account acc : trigger.New)
  	{
  		if(acc.BillingPostalCode != '' && zipRecords != null && zipRecords.size() > 0 && zipRecords.containsKey(acc.BillingPostalCode))
  		{
  			acc.ZipCodeField__c = zipRecords.get(acc.BillingPostalCode).id;
  		}
  		else if(acc.BillingPostalCode == '' && removedPostalCodes.contains(acc.BillingPostalCode)) // if Zip Code is remove, delink the ZIP lookup.
  		{
  			acc.ZipCodeField__c = null;
  		}
  	}
  }

Hope this helps !!!

Thanks,

Gaurav
skype: gaurav62990