SQL Server SELECT INTO @variable?

You cannot SELECT .. INTO .. a TABLE VARIABLE. The best you can do is create it first, then insert into it. Your 2nd snippet has to be

DECLARE @TempCustomer TABLE
(
   CustomerId uniqueidentifier,
   FirstName nvarchar(100),
   LastName nvarchar(100),
   Email nvarchar(100)
);
INSERT INTO 
    @TempCustomer 
SELECT 
    CustomerId, 
    FirstName, 
    LastName, 
    Email 
FROM 
    Customer
WHERE 
    CustomerId = @CustomerId

you can do this:

SELECT 
    CustomerId, 
    FirstName, 
    LastName, 
    Email
INTO #tempCustomer 
FROM 
    Customer
WHERE 
    CustomerId = @CustomerId

then later

SELECT CustomerId FROM #tempCustomer

you doesn't need to declare the structure of #tempCustomer

It looks like your syntax is slightly out. This has some good examples

DECLARE @TempCustomer TABLE
(
   CustomerId uniqueidentifier,
   FirstName nvarchar(100),
   LastName nvarchar(100),
   Email nvarchar(100)
);
INSERT @TempCustomer 
SELECT 
    CustomerId, 
    FirstName, 
    LastName, 
    Email 
FROM 
    Customer
WHERE 
    CustomerId = @CustomerId

Then later

SELECT CustomerId FROM @TempCustomer

If you wanted to simply assign some variables for later use, you can do them in one shot with something along these lines:

declare @var1 int,@var2 int,@var3 int;

select 
    @var1 = field1,
    @var2 = field2,
    @var3 = field3
from
    table
where
    condition

If that's the type of thing you're after