LINQ to SQL Left Outer Join

You don't need the into statements:

var query = 
    from customer in dc.Customers
    from order in dc.Orders
         .Where(o => customer.CustomerId == o.CustomerId)
         .DefaultIfEmpty()
    select new { Customer = customer, Order = order } 
    //Order will be null if the left join is null

And yes, the query above does indeed create a LEFT OUTER join.

Link to a similar question that handles multiple left joins: Linq to Sql: Multiple left outer joins

Not quite - since each "left" row in a left-outer-join will match 0-n "right" rows (in the second table), where-as yours matches only 0-1. To do a left outer join, you need SelectMany and DefaultIfEmpty, for example:

var query = from c in db.Customers
            join o in db.Orders
               on c.CustomerID equals o.CustomerID into sr
            from x in sr.DefaultIfEmpty()
            select new {
               CustomerID = c.CustomerID, ContactName = c.ContactName,
               OrderID = x == null ? -1 : x.OrderID };   

(or via the extension methods)