
I suppose it really won't do any good for me to tell you that this project can be _deadly_ and from your questions is probably not a good project to start out your electronics journey with.
The capacitors store enough energy to kill you several times over, not to mention other hazards like bits of metal spalling off and hitting you in the eyeballs, or other spectacular failure modes if you do something wrong, or even if you do it all right! Believe me, you do not want to be in the room when a 4700 uF electrolytic capacitor charged to 600 volts blows up from being reverse-volted.
And while a college lab might be able to get away with an open layout like that for a mains-connected voltage doubler capacitor discharge circuit... a hobbyist who does not yet know how to read a schematic probably should not even consider doing things like this.
All that being said, this is a fun project and I can understand why you want to do it. But how to approach it? It is a straightforward and simple circuit but there may be some problems.
First, you say you have a "bridge rectifier" and the video says they used a three-phase bridge rectifier module. But the schematic only indicates that half of a singlephase FWB is used (just two diodes.) So the first thing we need to find out is whether or not your actual bridge rectifier can be used as the schematic indicates, and I can't tell from the info provided.
Other than that, it is largely just a matter of putting wires together as the schematic indicates. The lines indicate wires, dots indicate connections, the black dots on the transformer symbols indicate the "start" of the windings, the + and - symbols indicate anode (triangle) and cathode (bar) of the diode symbols. But you should think seriously about the layout and safety. Your layout absolutely must protect the terminals of the capacitors and all wiring from possible shorts or inadvertent contact with living things. Your wiring has to be sturdy, well insulated, the leads from the caps and SCR to the launch coil should be heavy and short, the connection to the mains should be fused or protected with circuit breaker (you could use a good quality power strip with breaker) and you should NOT operate or test this thing while alone. Have somebody there to put out the fire and call the ambulance. And I am only half kidding.
In case it didn't sink in the first time, this project can KILL YOU DEAD. No mistakes allowed. Imagine that HDD platter embedded in your forehead.