You're looking for pivot_table:
In [11]: medals = df.pivot_table('no of medals', ['Year', 'Country'], 'medal')
In [12]: medals
Out[12]:
medal Bronze Gold Silver
Year Country
1896 Afghanistan 3 5 4
Algeria 3 1 2
and if you want to reorder the columns:
In [12]: medals.reindex_axis(['Gold', 'Silver', 'Bronze'], axis=1)
Out[12]:
medal Gold Silver Bronze
Year Country
1896 Afghanistan 5 4 3
Algeria 1 2 3