Test Bench simulation

a forum will help you to solve particular issues, not general working 
principal

better get a book for basic knowledge or study it at university

this could be your code

nd if you are very new to this field then force values directly in wave 
form and check results


library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.STD_LOGIC_ARITH.ALL;
use IEEE.STD_LOGIC_UNSIGNED.ALL;

entity DataGen is

    Port ( Input : in  STD_LOGIC_VECTOR (1 downto 0);
           CLK, Reset : in  STD_LOGIC;
           Output : out  STD_LOGIC_VECTOR (15 downto 0));

end DataGen;

architecture Behavioral of DataGen is
signal counter : STD_LOGIC_VECTOR (1 downto 0);

begin

process ( Reset, CLK )
begin
  if Reset = '1' then -- If the reset button is pressed it clears
  Counter <= "00";    -- the Counter value and sets it to 00

  elsif CLK'event and CLK = '1' then -- Used for Mode 1,2,3; Increments 
the value of Counter
    Counter <= counter + '1';      -- each time the CLK singal is 1 
therefore creating an endless
    if Counter = "11" then        -- loop for Counter
    counter <= "00";

    end if;
  end if;

end process;


process ( Input, CLK, Reset, Counter )

begin

  if Reset = '1' then -- Resets the 7-segment display if Reset is 1
    Output <= X"0000";

  elsif CLK'event and CLK = '1' then
    --Mode 0
    if Input = "00" then --if selected it will display A5A5
    Output <= X"A5A5";

    --Mode 1
    elsif Input = "01" then -- if selected will display 1 to F 
continously
      case Counter is

      when "00" => Output <= X"0123";
      when "01" => Output <= X"4567";
      when "10" => Output <= X"89AB";
      when "11" => Output <= X"CDEF";
      when others => Output <= X"0000";

      end case;

    -- Mode 2
    elsif Input = "10" then --if selected will display 500662 
continously
      case Counter is

      when "00" => Output <= X"5006";
      when "01" => Output <= X"6250";
      when "10" => Output <= X"0662";
      when "11" => Output <= X"5006";
      when others => Output <=X"0000";

      end case;

    -- Mode 3
    elsif Input = "11" then --if selected will display 503188 
continously

      case Counter is

      when "00" => Output <= X"5031";
      when "01" => Output <= X"8850";
      when "10" => Output <= X"3188";
      when "11" => Output <= X"5031";
      when others => Output <= X"0000";

      end case;
    end if;
  end if;
end process;
end Behavioral;

Small optimization, please use
use IEEE.mumeric_std.ALL;

instead of

use IEEE.STD_LOGIC_ARITH.ALL;

because different tools can interpret std_logic_arith different. There 
should be no drawbacks with numeric_std.