Combining Two Base Tables with a 1:M relationship Into One View with Distinct Rows
You will need to use the PIVOT function with a INNER JOIN to accomplish this:

SELECT StudentId
     , FName
     , LName
     , CASE H WHEN 0 THEN NULL ELSE 'H' END AS [Hispanic]
     , CASE W WHEN 0 THEN NULL ELSE 'W' END AS [White]
     , CASE B WHEN 0 THEN NULL ELSE 'B' END AS [Black]
     , CASE A WHEN A THEN NULL ELSE 'A' END AS [Asian]
     , CASE I WHEN 0 THEN NULL ELSE 'I' END AS [Indian]
 FROM (SELECT s.StudentId, FName, LName, r.[Race Code]
         FROM [Students] AS s
         JOIN [Race] AS r ON r.StudentId = s.StudentId)
PIVOT (COUNT([StudentId])
         FOR [Race Code] IN ([H],[W],[B],[A],[I])) AS p


If you are happy with just having the count as the row values then there is no need for the case statements and the query can be simplified to this:

SELECT StudentId
     , FName
     , LName
     , [H] AS [Hispanic]
     , [W] AS [White]
     , [B] AS [Black]
     , [A] AS [Asian]
     , [I] AS [Indian]
 FROM (SELECT s.StudentId, FName, LName, r.[Race Code]
         FROM [Students] AS s
         JOIN [Race] AS r ON r.StudentId = s.StudentId)
PIVOT (COUNT([StudentId])
         FOR [Race Code] IN ([H],[W],[B],[A],[I])) AS p