How do I declare and assign a variable on a single line in SQL

Here goes:

DECLARE @var nvarchar(max) = 'Man''s best friend';

You will note that the ' is escaped by doubling it to ''.

Since the string delimiter is ' and not ", there is no need to escape ":

DECLARE @var nvarchar(max) = '"My Name is Luca" is a great song';

The second example in the MSDN page on DECLARE shows the correct syntax.