One (usually fast) way would be group by:
insert  NewTable (ColumnA, C1, C2, C3, C4)
select  ColumnA
,       IsNull(max(case when ColumnB = 'C1' then 'Y' end), 'N')
,       IsNull(max(case when ColumnB = 'C2' then 'Y' end), 'N')
,       IsNull(max(case when ColumnB = 'C3' then 'Y' end), 'N')
,       IsNull(max(case when ColumnB = 'C4' then 'Y' end), 'N')
from    OldTable
group by
        ColumnA
Another way is subqueries, like:
insert  NewTable (ColumnA, C1, C2, C3, C4)
select  src.ColumnA
,       case when exists (select * from OldTable ot 
                          where ot.ColumnA = src.ColumnA and ot.ColumnB = 'C1') 
                  then 'Y' else 'N' end
,       case when exists (select * from OldTable ot 
                          where ot.ColumnA = src.ColumnA and ot.ColumnB = 'C2') 
                  then 'Y' else 'N' end
,       case when exists (select * from OldTable ot 
                          where ot.ColumnA = src.ColumnA and ot.ColumnB = 'C3') 
                  then 'Y' else 'N' end
,       case when exists (select * from OldTable ot 
                          where ot.ColumnA = src.ColumnA and ot.ColumnB = 'C4') 
                  then 'Y' else 'N' end
from    (
        select  distinct ColumnA
        from    OldTable
        ) src
Or, adapted from Chris Diver's answer, with pivot:
select  ColumnA
,       case when C1 > 0 then 'Y' else 'N' end C1
,       case when C2 > 0 then 'Y' else 'N' end C2
,       case when C3 > 0 then 'Y' else 'N' end C3
,       case when C4 > 0 then 'Y' else 'N' end C4
from    OldTable src
pivot   (
        count(ColumnB)
        for ColumnB IN ([C1], [C2], [C3], [C4])
        ) pvt