Whenever customer record is updated, before updating the record create new record in test object with old values of customer record.

try with below code. modify the field api Names and object names

trigger testrecordinsert on customer__C (before update) {
List<test_object__c> inserttestrecords = new List<test_object__c>();
for(customer__C ctr:trigger.old){
test_object__c to = new test_object__c();
//you assign the list of fields you want to insert in the object from customer__c object.
to.Name = ctr.name;
to.field1__c = ctr.field1__c;
to.field2__c = ctr.field2__c;
inserttestrecords.add(to);
}
insert inserttestrecords;
}