as mentioned in the first link you need reagents (buffer including Mg2+, enzyme (taq polymerase), nucleotides, primers), no idea where you can get them as a private person. Finally you have to prepare (isolate) DNA, for this quite good protocols using household reagents exist.
And finally to make it visible usually gel electrophoresis (usually agarose gels (a polysaccharide matrix) in special gel chambers were DNA is separated by charge and size using an electrical field and then dyed and made visible e.g. by UV light. For this surely home made solutions (e.g. usig filter papers) exist too.
Not really sure if these devices will really work, especially the one in the first link seems to slow for a good working PCR, i.e. the system is too slow heating and especially cooling down again the water bath (professional thermal cyclers heat and cool at a rate of several degrees Celsius per second!). To have separate chambers with a fixed temperatures (three for denaturating, annealing and elogation) is much easier and reliable. Then you switch the tubes between chambers manually and have a fast and accurate temperature ramps too (the first professional machines worked similar).
The second machine looks better but haven't looked in the details.
One must presume that long and short arguments contribute to the same end. - Epicurus
...except casandra's that did belong to the funniest, most interesting and imaginative (or over-imaginative?) ones, I suppose.