[SalesForce] SOQL Query for month operator

Visitor should be Visitor__c. All custom objects are suffixed with __c, as should all of your custom fields on either standard or custom objects. So, your code would look something like this:

Visitor__c newVisitor = new Visitor__c ();
newVisitor.Name = 'John Smith';
newVisitor.Identifier__c = 'john@somewhere.com';
insert newVisitor;

Only standard fields are not suffixed with __c, e.g. Name, Id, CreatedDate etc.

EDIT: boots and braces with Try/Catch

See the docs for a full description of the Insert operation:

http://www.salesforce.com/us/developer/docs/apexcode/Content/apex_dml_insert.htm

Doing a DML insert/update/upsert could result in an exception depending on a number of factors:

• It could be that the operation will mean that you exceed a Governor limit (see
  http://www.salesforce.com/us/developer/docs/apexcode/Content/apex_gov_limits.htm). If you are inserting multiple records, 'bulkification' will most likely be required to prevent this.
• It could also (and more likely) be caused by an issue with the record that you are trying to insert (e.g. missing required field, failed validation etc.).

Surrounding your operation with a Try/Catch is always good practice and will allow you to fail gracefully should the worst happen. Note, you cannot fail gracefully with a Try/Catch for a Governor limit issue.

There are essentially two ways to Try/Catch for DML statements (sorry, formatting has gone screwy):

This will suffice for a single record (though you could use the second option here too):

try
{
    insert newVisitor;
}
catch( DmlException ex )
{
    // fail gracefully
}

This may be preferable for multiple records, where the 'false' parameter indicates that this is (not) an 'all or nothing' insert:

Database.SaveResult[] MySaveResult = Database.Insert(newVisitors, false);
for (Database.SaveResult sr : MySaveResult) {
    if (!sr.isSuccess()) {
        // Operation failed, so get all errors                
        for(Database.Error err : sr.getErrors()) {
            System.debug('The following error has occurred.');                    
            System.debug(err.getStatusCode() + ': ' + err.getMessage());
            System.debug('Fields that affected this error: ' + err.getFields());
        }
    }
}

I'm guessing you've adapted this code from elsewhere, as the constructor for the Summary class expects a parameter of type AggregateResult:

public Summary(AggregateResult ar) {
    ID = (Integer) ar.get('ID');
    // etc.

Aggregate results are used when you use aggregate functions in SOQL, such as SUM(). Your SOQL query doesn't contain any aggregate functions and so returns a list of Incident__c records which you're storing in the list results. Since you want to create summaries for each of these records you need to adapt your constructor accordingly (or even overload it, which means adding a second constructor that takes different parameters):

public class Summary {
        public String ID{ get; private set; }
        public String INCNAME{ get; private set; }
        public String RepName{ get; private set; }
        public String RepId{get;private set;}

        public Summary(Incident__c i) {
        ID = i.Id;
        INCNAME= i.Name;
        RepName = i.Rep_Lookup_id__r.Name;
        RepId = i.Rep_Lookup_id__c;
    }
}