Well, strictly speaking no one can directly see alpha particles because they are too small. But one can see result of interaction of particle with macro objects and observe visible traces of such interaction. Easy and spectacular way is to observe tiny light flashes appearing at scintillator with every hit. A scintillator is a material that exhibits scintillation — the property of luminescence when excited by ionizing radiation. Luminescent materials, when struck by an incoming particle, absorb its energy and scintillate, (i.e., re-emit the absorbed energy in the form of visible light). Best scintillator for this Instructable is zinc sulfide (ZnS), which is also one of the oldest known. Sir William Crookes used it for the same properties in 1903. This substance is not expensive, but there are very few places to buy it. Good source for such scintillator is old TV Cathode ray tube. And black-and-white CRT is better than color tube. For alpha particles source I use smoke detector ionization chamber. You even don't need to destroy whole smoke detector, chambers may be bought separately and much cheaper. Mine is HIS-07 with small amount of Americium 241.
It is important to mention that scintillations are very faint, observation must be done in a completely dark room after your eyes will become sensitive enough, and usually it takes 10-30 minutes. Well, many sources says 30 minutes, but I will say after 10 minutes you may start to see scintillations, and after 30 minutes you will see them much more sure.
Step 1: CRT Preparation
I was lucky to buy small (4inch, 100mm) black-and-white TV tube on local flea market for only 2$.
I think oscilloscope tube will also do well.
First, carefully broke the CRT "tail", you will hear how air is going inside the empty CRT body. Wear protective glasses. Trim back cone of CRT with wire cutters. The hole must be about 15mm in diameter.
Disassembling ionization chamber is also very easy, when you will hold it in hand it will be clear. On third pic you may see alpha source itself.
Attach obtained source to some long rod, i used some paper tube.
Now, in the completely dark room, if you place alpha particle source attached to a rod inside the CRT, near (10-20mm) the screen from the back side, with the naked eye you will see faint spot of light.
On the picture which appears completely dark I've try to show this. You may see square contour of the CRT and faint white spot.
Step 2: Use 10x Magnifier
Now, let's try to observe single flashes with the help of 10x magnifier.
In left hand hold tube with the alpha source inside it, in right hand took loupe. It is quite difficult to centre your eye on loupe in total dark and to keep focus. So make some tests with lights on. After 10 minutes in dark you will see absolutely amazing view of thousands tiny flashes appearing and immediately disappearing every second. I guess it is impossible to record video of this, but I've found on YouTube mathematical simulation. It gives very realistic view.