Attachments for a list item are stored as SPFile objects under a hidden folder in the list where those attachments are stored. Each list item that has an attachment has its own folder with the ID of the item being the folder's name. Here is a code sample to copy attachments from one item to another:
private void CopyAttachments(SPListItem sourceItem, SPListItem targetItem)
{
//get the folder with the attachments for the source item
SPFolder sourceItemAttachmentsFolder =
sourceItem.Web.Folders["Lists"].SubFolders[sourceItem.ParentList.Title]
.SubFolders["Attachments"].SubFolders[sourceItem.ID.ToString()];
//Loop over the attachments, and add them to the target item
foreach (SPFile file in sourceItemAttachmentsFolder.Files)
{
byte[] binFile = file.OpenBinary();
targetItem.Attachments.AddNow(file.Name, binFile);
}
}