First you need something radioactive
Polonium-210 is the generally well known isotope of Polonium (the one used to kill traitorous Russians, etc) and has a half-life of 138 days. There are three other isotopes with half-lives over 1 day; Po-209 with half-life 135 years; Po-206 with a half-life of 2 years; and Polonium 206 with half-life 6 days. The problem with Po-209 is that to get it naturally you have to induce mostly stable Bismuth-209 to beta decay to get it, and the problem with Po-208 and Po-206 is you need completely stable lead to beta decay to get it. So both those isotopes are out.
Po-210 however is a byproduct of the Uranium decay chain. That is, when U-238 decays, it passes through Po-210 at some point. So we have something to work with there.
The Uranium decay chain
Since its linked above, you should take a look at it. The characteristics of the various elements are relevant, since that will determine if it kills you or takes forever to make the next element.
First off, several steps on that chain are deadly. You can get decay radiation levels from a chart of nuclides. For example, Bismuth-214, a step in the chain down to Po-210 decays with a half-life of 20 minutes releasing a scattering of MeV range gammas as it goes. If you managed to make a gram of it in your basement lab, even if it is in a lead box, you will probably have just killed your whole family over the course of the next hour or two.
Next you have to worry about the slow steps in the decay chains. For example, after Uranium-238 decays, a few steps down is Thorium-234, which itself takes 2.5×105 years to decay. Thats a bit long to wait. So we need to have massive quantities of uranium in order to get a usable amount of polonium. The decay fraction of Po-210 is about 10−10; that is for every 1010 units of Uranium, you would expect to find 1 unit of Polonium. If you want 1 mg of Polonium, then you need to start with about 10 tons of Uranium, and extract every last molecule of Polonium.
By refining Uranium
One way to do this in your basement is the exact same way that Marie Curie and Andre-Louis Debierne did it in the early 1900s. They started with pitchblende, a Uranium ore that can be up to 80% U by mass. This they powdered and washed in sulfuric acid, causing both the radium and polonium content to form sulfates and enter solution. By drying the solution, you now have both substances in residues. They can be separated by boiling in sodium hydroxide and then washing in hydrochloric acid and separating using fractional crystallization. This is the method that the Manhattan Project used to make Polonium as part of the trigger device for the first nuclear weapons. According to some sources, they were able to turn 37 tons of purified uranium ore into 9 grams of Polonium. Marie Curie had to use similar quantities of Uranium to get Radium and Polonium.
This process is simple but time consuming and energy intensive. The good news is that in addition to polonium, with sufficient chemical knowledge you can get Radium and Lead-210. But there are several drawbacks. First, Marie Curie died of radiation poisoning, and her notes are kept in lead boxes since their activity is so high...so this is a dangerous process. Second, there may be issues with getting your hands on 10 tons of pitchblende. I imagine there are non-proliferation agreements that would make this nearly impossible for radiation-hackers.
By breeding Bismuth
The other method for making Polonium is by taking Bismuth-209 and firing neutrons at it until one sticks making Bismuth-210. Bismuth-210 has a half-life of 5 days, so if you can make a good amount of Bismuth-210, then in 25 days almost all of it is now Polonium, and only about 6% of the Polonium has decayed.
While getting Bismuth-209 isn't that hard, achieving a high neutron flux is. One method is by mixing your Bismuth with a neutron emitting substance. Unfortunately, things emit neutrons only when they really don't want that neutron in the core (like the extra neutron stuck to an alpha particle in Helium-5), so making these substances is nearly impossible and they stick around for milliseconds at best.
Another option is the flux generated in a nuclear reactor. While that is difficult for obvious reasons, there is another alternative, which is the neutron flux generated in a sub-critical mass of a fissile material, like U-235 or Pu-238. For these fissile materials that can sustain a chain reaction, a sub-critical mass will generate a large neutron flux in the volume of the mass. So if you took two slabs of Plutonium, smooshed them around a block of Bismuth with a vice, you would get Polonium-210.
Again, the problems here are many: the high neutron flux from the Plutonium will affect nearby living creatures as well as the Bismuth, and getting your hands on a kg or so of fissile material is probably even harder than the 10 tons of purified uranium ore.
Why don't we skip Polonium?
If the goal is to get radioactive things to play with and show off, Polonium is a tough sell. There are other radioactive materials that would be easier to separate.
First, there is Radium, which I mentioned before. It has a half-life of 1600 years so it is more common, more stable, and less dangerous than Polonium. You make it the same way you make polonium, and there is about 4 orders of magnitude more of the stuff than polonium in uranium ores. That means you could get a milligram from only 1kg of pure Uranium ore, at 100% processing efficiency, or maybe 10 kg of pitchblende. Radium also has some nice side-attributes such as decreasing solubility of radium chloride with increasing concentration of hydrochloric acid. Thus, when soaked in a concentrated HCl bath, the radium precipitates as radium chloride salts while most other metals and minerals get dissolved.
Another option is Radon gas. This has a much shorter half-life of 3 days, shorter even than Polonium. But has the unique properties of being both a gas and noble, meaning it is chemically inert. Radon gas can be released from uranium ores by crushing and dissolving in HCl. Then the other gas byproducts can be reacted out using copper and various compounds until only the radon is left. This is much faster than the tedious fractional crystallization method. Also, radon exists in nature in places; my house has a radon control system that vents my basement to make sure no radon builds up. If you can find a naturally radon-dense location like the Watras home, you could attempt to separate the radon diretly from the air by gas chromatography. Radon-222 is much heavier than pretty much any other gas you will find.
The problems for both methods stem from two things: danger to the experimenter and difficulty of obtaining materials. Of all the things I mention above two scenarios seem the most likely:
The 'makers' have some ally (maybe one of the makers works at a uranium refining facility?) that can get them the concentrated fissile material like U-235 needed to breed Polonium from Bismuth at home. Obviously, there are security issues to be overcome, many people will likely have to be in on the deal.
The 'makers' are satisfied with radium, and are able to gather a few hundred kg of less concentrated uranium ores and perform the Curie process at home to make a few mg of Radium. Preferably with more safety precautions taken.