Of course this is for fun only as traps are illegal.
I used a few modern pieces of kit for convenience and illustration purposes.
The mechanism is simple. A small perch is wedged in a hole against a piece of string with a heavy weight attached at one end and a noose on the other. The weight pulls the peg into the hole using the friction of the string, The tighter the peg goes in, the more the string is trapped! The noose sits on the peg.
When a bird alights on the peg it (the peg) comes out of the hole, the string is not held anymore and the weight drops tightening the noose tightens around the birds legs.
Again, this is for fun and learning only as they are illegal in normal circumstances.
An old hearth board was used for the peg board.
The peg was an old spindle which means it fits perfectly in the hole in the board.
A good heavy rock. Make sure it is held high enough over the ground so that when the trap is sprung it doesn't hit the ground before the noose tightens.
All assembled with rock at great height. Test it a few times to make sure it all comes together. This trap really has a hair trigger.
Thanks for looking,