You should use the InsertOnSubmit method:
NorthwindDataContext context = new NorthwindDataContext();
context.Products.InsertOnSubmit(new Product(..));
context.SubmitChanges();
The Add method exist on the EntitySet members, is mostly used when adding Child entities to a Parent one, for example:
var category = new Category{ Name = "Breveages"};
category.Products.Add(new Product{ Name = "Orange Juice"});
category.Products.Add(new Product{ Name = "Tomato Juice"});
category.Products.Add(new Product{ Name = "Cola"});
//...
context.Categories.InsertOnSubmit(category);
// This will insert the Category and
// the three Products we associated to.
EDIT: To do update operations, you just need to retrieve the entity by doing a query, or attaching it, for example:
var customer = context.Customers.Single( c => c.CustomerID == "ALFKI");
customer.ContactName = "New Contact Name";
context.SubmitChanges();
The DataContext tracks the changes of its related entities and when the SubmitChanges method is called, it will detect that change, and generate an Update SQL statement behind the scenes to do the update operation...