Salesforce provides an example of an after insert trigger in the following link http://help.salesforce.com/HTViewSolution?id=000181538 . Here is the answer they provide.

A trigger can be written on Attachment using Force.com IDE or ANT.

A sample code would be:

    trigger SetTitleToAttachment on Attachment (after insert) {

    String Title;
    Id pId;

    for(Attachment att: Trigger.new){
    Title=att.Name;
    pId=att.ParentId;
    }

    List<Case> c=[select Id , Title__c from Case where Id=:pId];

    //assuming one record is fetched.
    c[0].Title__c=Title;

    update c[0];
 
    }

Note: There is no way to write a trigger using the Salesforce.com UI (Portal).