RS232 rxd code

Start by drawing your design. The www can help you. Use your favorite search engine and search for UART or rs232.

Probably further details ie block diagram would be helpful to illustrate your target implementation.

library ieee;
use ieee.std_logic_1164.all;
--here, there is one more "use ieee" that i do not remember (not numeric)
entity rxd is
port( out1: in std_logic; --clock 9600hz
         rxd: std_logic;
         led: std_logic; --to check if the data "00111111" is recieved
       );
end entity;
architecture arc_rxd of rxd is
signal cnt: integer:=0; --to check the 8 bit of data
signal word: std_logic_vector(7 downto 0); --to put the data in signal
type state_type is(start_bit,check_bits,stop_bit,data_out);
signal state: state_type;
begin
process(out1,rxd)
begin
          if(out1='1' and out1'event)then
              case state is
              
                     when start_bit =>
                            if(rxd='0')then -- check start bit
                              state<=check_bits;
                            elsif(rxd='1')then
                              state<=start_bit;
                            end if;
                    when check_bits =>
                              cnt<=cnt+1;
                            if(cnt<8)then
                              word(cnt)<=rxd;
                            elsif(cnt=8)then
                              state<=stop_bit;
                              cnt<=0;
                            end if;
                   when stop_bit =>
                            if(rxd='1')then
                 state<=data_out;
                            end if;
               when data_out => --this state check if the data "00111111" is recieved
                          if(word="00111111")then 
                       led<='1';
                        else
                       led<='0';
                       state<=start_bit;
                         end if;
              end case;
         end if;
end process;    

Then you compare the received bits with a bitmask for your char. Or am I missing something?

Have you run a simulation?

The bit takes time to send. So you need to check your bit in the middle of that duration so you know for sure what bit you read. On the edges gives inacurate readings. Also, you need to pass your signal trough a synchronizer to prevent metastability.