the idea for this comes from the stars. A star is concentrated hydrogen. Under the load of gravity, the hydrogen builds up pressure, which eventually builds up high temperatures. How high? Very high! Some millions of degrees. Under these pressures and temperatures, the hydrogen molecules fuse together and they create heavier elements (starting from helium). This fusion has the characteristic that 2 atoms of hydrogen (1+1) build something that does not weight 2, but instead it weights 1.95. The other 5% is energy emitted. This is what they want to achieve. They will use ridiculously powerful lasers. The beams will be concentrated into a point of some microns, and the temperature will rise up to 150x106 degrees Celsius. This will convert deuterium and tritium (some hydrogen isotopes) into plasma. Some big electromagnets in the middle of the device will hold the heated plasma concentrated in the middle.
As far as i understand, there are 2 dangers for this experiment. First of all, the amount of energy that such a device can generate is huge! So if something goes wrong, i suppose that the explosion will be epic, yet again only dangerous for the (not so close) neighbors. I am not sure if there will be radioactive materials. Normally there should not be any, since the first thing generated by this device will be helium. Stars continue making heavier elements than helium (lithium, beryllium, boron, carbon) up to iron, but to fuse helium together to make lithium requires much higher energy levels, the heavier the atoms the higher the energy. In stars, efficiency is not a factor, but for us it is, so i think that the fusion will end at helium. But as a byproduct, there will certainly be radiation. Atom fusion generate many different radiation wavelengths (alfa-beta-gama-x). Maybe someone who knows chemistry/physics can answer to this question: What will happen with this radiation?
As for the black hole: A black hole requires MASS! MASSIVE MASS! The mass of our sun is not enough to form a black hole. Our sun will die quietly as a white dwarf. Black holes exist usually in the center of galaxies and in places where huge stars died. It is most possible that you re-discover the flux capacitor and mod your car into a flying Deloarean to visit the black hole in the center of our galaxy some 30.000 light years away), rather than this experiment generate a black hole and swallow us in hell.