You don't need to change the isolation level. An UPDATE lock is a read lock which means "I intend to update this row/page/table". Readers are not blocked by this lock, but only one process can hold an UPDATE lock on a resource.
Normally, SQL Server takes out an UPDATE lock without you have to ask for it, for instance when it is in the process of locating rows for updating.
However, you can yourself add the hint UPDLOCK to require an UPDATE lock. Say that you have some piece of code where you do:
SELECT @val1 = col1, @val2 = col2, ... FROM tbl WHERE keycol = @keyval
-- Some complicated computation here.
UPDATE tbl SET resultcol = @result WHERE keycol = @keyval
You may be anxious that another process may update the row while for @keyval while you are making the computation, which could lead to that you update the row with an incorrect value.
You can prevent this from happening this way:
BEGIN TRANSACTION
SELECT @val1 = col1, @val2 = col2, ... FROM tbl WITH (UPDLOCK) WHERE keycol = @keyval
-- Some complicated computation here.
UPDATE tbl SET resultcol = @result WHERE keycol = @keyval
COMMIT TRANSACTION
You need to wrap the operation in a transaction, or else the lock will be released. But you don't need to change the isolation level explicitly. The UPDLOCK hint, however, implicitly sets the isolation level to REPEATABLE READ for tbl. (But not any other tables you may read in the computation.)