I know that when an anode & cathode are placed inside a vacuum tube, electrons are emitted from cathode and goes towards anode.
How to produce such a high voltage?, How to create such a vacuum tube?
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I used to make X-ray tubes for a living... and the "right" answer to this question would run the length of a book.
So just a few pointers. I don't expect that you would be able to create an electron tube after this - at least not one that lasts. Note also that if you do get it to work, it will produce dangerous (X ray) radiation. And unless you understand the thermal physics very well before you turn it on, there is a good chance it will overheat and explode, sending broken glass everywhere. In short, this is a "children don't try this at home" story.
To create an electron beam, you need high voltage, insulation and vacuum. The latter two of these things can be provided by a glass tube.
Problem #1 - making a tube of the right size. This requires glass blowing; you might want to use Pyrex glass because it is tough and won't crack easily under thermal stress, but it is hard to blow. Find a glass blower who will create an envelope strong enough to withstand the pressure of the atmosphere (1 bar is approximately equivalent to the weight of 1 kg per square cm of tube). Leave the ends open, we need them for the electrical connections. Also leave a little tube sticking out of the side for the vacuum pump.
Problem #2 - make electrical connections. Usually, one uses a Coolidge tube: a hot filament emits electrons (think of them as "boiling" out of the metal as the metal is heated). You might want to sacrifice an incandescent light bulb to get a filament. Cool side note: Coolidge worked for General Electric and had solved the problem of making ductile tungsten, the material used to make light bulb filaments. He soon figured out they would make good Xray tubes, and to this day the most common tube design is similar to the one he invented about 100 years ago. This is also how GE got into medical imaging - today they are one of the largest manufacturers of medical imaging equipment. Figure out how to attach the filament (leave it attached to its socket) to the rest of the bulb - not having to think about how to make an electrical connection through a glass tube saves you years of development time... again your friend the glass blower can help you connect the two together.
Problem #3 - make an anode. While the cathode is relatively easy (because you can pilfer bits from an incandescent bulb), the anode is harder because it will be bombarded with high energy electrons and get VERY HOT. So hot, that if you are not careful you will evaporate the metal in an instant. Make it out of a piece of copper (good thermal conductivity) and keep the beam power to a few W and you will be OK. Figuring out how to put the copper inside the glass envelope and sealing the glass around it is VERY HARD. Typically you would draw the end of the copper to a thin rod (just strong enough to hold the anode) which would be welded to a piece of KOVAR - a material with the same thermal expansion as glass. Now making the connection between kovar pins and glass vacuum tight is very hard; again, you might want to pilfer bits from a light bulb since the surface treatment needed to get the glass to stick to the metal is challenging (and uses some toxic acids).
Problem #4 - evacuate the tube. It is not enough to suck the air out: as soon as you start heating the anode, it will start outgassing and the vacuum will be lost. In the process the tube will become unable to hold a high voltage. So you have to pump the air while operating the tube to get a sufficient vacuum. This combined processing is something that takes lots of fine tuning...
Problem #5 - sealing the tube. This is relatively easy. Remember the little glass tube that was sticking out of the side in step 1? Just heat that tube with a gas flame while the vacuum pump is running. As the glass gets soft, the tube collapses on itself and seals the tube. Of course if you overdo it, the tube imploded.
Did I mention "don't do this at home"? And if you do, wear a full face protection and gloves. Oh - and you can't "see" that glass is hot - so after you melt it and it looks "not hot" (not red) any more, don't touch it. It will melt your skin off.
Problem #6 - you really need to solve this before you get the vacuum going: generating a high voltage. This can be quite easy. A hot cathode tube is actually a rectifier, so you can just use a high voltage transformer with a decent voltage rating and drive it with a low(er) voltage AC; that voltage will "step up" according to the transformer winding ratio. You do need to be careful that the wires are kept well away from each other as they might arc if they get too close (depending on the voltage you use). Again, people have made careers out of making HV cables; don't expect that your Radio Shack wire will just work for you. If you can find high voltage rectifiers, you could actually rectify the output of your HV generator. There are other methods to generate high voltages - including mechanical techniques (like Van de Graaff generator) that produce high voltages at low currents.
Problem #6b: you also need a (small) ac voltage to heat the cathode; this can be provided by a small filament transformer that has good insulation between primary and secondary (since the primary will be at normal potential, but the secondary will float at cathode potential). You need to have a way to regulate the cathode (filament) current in order to control the over all current through the tube.
Connect it all together and stand well clear. Don't be disappointed if the first ten years of trying this don't work. You are in illustrious company.