Content type does not contain a column, or field. It only contains a reference to a site column or field. Therefore you should create a site column before you can add it to the content type definition.

The field reference in content type are managed through SPFieldLink object.

Add field reference from Content Type:

public static void AddFieldRefToContentType(SPContentType contentType, SPField field)
{
    //Check if the Field reference does not exists already 
    if (!contentType.Fields.ContainsField(field.Title))
    {
         contentType.FieldLinks.Add(new SPFieldLink(field));
         contentType.Update();
    }
    else
    {
         //Do Nothing
    }
}

Delete field reference from Content Type:

public static void DeleteFieldRefFromContentType(SPContentType contentType, SPField field)
{
    //Check if the Field reference exists
    if (contentType.Fields.ContainsField(field.Title))
    {
         contentType.FieldLinks.Delete(field.Title);
         contentType.Update();
    }
    else
    {
         //Do Nothing
    }	
}

Check MSDN information for more details on Field and Field References.