Vhdl codes for counter to start and purse

The best way to achieve what you are asking is to draw yourself a flow chart. If you are looking for an on/off button with just one push then you would have something like this.

process(clk) begin
  if(rising_edge(clk)) then
     button_prev <= button_curr;
     button_curr <= button;
  end if;
end process
Button_pulse <= button_curr AND (NOT button_prev);

Now, you can register the pulse, add debounce, ect. It is up to you.

Next, you need to create a state machine to handle the enable to your counter. From what you've described you have 2 states, on and off. you start in the off state, if the button_pulse = 1 then you go to the on state and again if the button pulse is 1 you go back to the off state. Then you describe your counter enable as 1 when in the on state and 0 when in the off. I recommend drawing this out and then creating your state machine to match your diagram.