Anything with an atomic number greater than 92 (Uranium), is called transuranic. These elements are manmade, but is there a difference in any way besides that? How are these elements created?
We generally call the transuranics "man-made" elements because they are normally not found in nature. However, it has been verified that some of these elements are produced and found in nature in very small amounts. It's likely that all of them (and maybe more) exist somewhere in the universe, but the only way to get them in any useful amounts is to make them yourself.
You asked a couple questions, let's look at them separately.
First, there is nothing inherently different about transuranic elements. They do share some common characteristics. As a class, they are all radioactive. But that's also true of all elements above atomic number 82 (lead) (Pb-208 being the heaviest stable isotope known). And radioactivity is actually far more common than stability if you look at all the known nuclides. The transuranics also share the trait that they will undergo nuclear fission. We'll look at that later, also check the link for more info. But these traits are not unique to the transuranics. Uranium is also fissionable, and elements as light as atomic number 88 (radium) may undergo fission (but not very efficiently). We also should keep in mind that there are many isotopes that are much lighter than uranium which are only available by "artificial" means. So, again, there's no unique property that applies only to "man-made" isotopes or transuranic elements.
Secondly, you asked how these elements are created. The short answer is that they are produced in particle accelerators and nuclear reactors. For the long answer, let's examine the actual process of how they are made. Let's think for a moment how we would create any element - whether it be transuranic or otherwise.
Atoms are collections of neutrons and protons (with some electrons attached to complete the picture). As you probably know, changing the number of protons changes the element. So an atom with one proton (regardless of how many neutrons it has) is hydrogen, an atom with two protons is helium, etc. So if I want to create atoms with, say 10 protons, I have to figure out a way to get ten protons together along with enough neutrons to keep those protons together. It seems logical that the easiest way to do that might be to start with atoms having nine (or maybe eleven) protons, and see if I can add (or subtract) one from there. So, I need to cause a nuclear reaction, or change. Nuclear changes take lots of energy, because there is tremendous force (called, the strong force) holding nuclear particles together. This is different than chemical reactions - which only involve electrons. Electrons aren't held in atoms with nearly as much force as nucleons, so there's not as much energy needed to rearrange them. So, we have to impart energy to the nucleus. This is done by hitting it with something. Now, nuclei are very selective about what they will allow themselves to be hit by. They have a kind of "energy shield" around them. To get past this shield, other particles generally need lots of energy. So, one way to hit the nucleus is to raise the energy of some particles high enough to do that, and fling them at the nucleus - a particle accelerator. The idea is basically to shoot particles at a particular target material having properties that will result in the desired product material. Some particles work better for this than others. Very high energy photons (extremely energetic x-rays) will also do this - but you need an accelerator to produce these photons. So, particle accelerators like Jefferson Lab can and do change the nuclear structure of the materials exposed to the particle beam. This is how many of the radio-isotopes for pharmaceutical use are made. In the case of some of these rare isotopes, there is only one facility (a National Laboratory accelerator) at which the material is produced.
Now, another way to impart energy to the nucleus is to present it with a gift - a package of energy which it will eagerly accept without having to "force" the package in. The particle that best meets this description is a neutron. Now, not every type of atom will accept a neutron gift, but a significant number of them are more than willing to gobble up free neutrons if they are available. The result of absorbing the neutron depends on the type of atom that does the absorbing. And, if we want this reaction to take place at a rate which is useful, we have to make sure there are plenty of free neutrons available. Let's go to an example that fits your question. We want to make transuranics. Let's start with uranium. If I dig uranium ore up out of the ground, over 99% of it is uranium 238, which has 92 protons and 146 neutrons. U-238 has a reasonable attraction for neutrons. Now, let's suppose we can expose our sample of U-238 to plenty of free neutrons. Some of the U-238 atoms will absorb neutrons, turning them into U-239. Now, U-239 is radioactive, and undergoes beta decay (its half-life is about 23 minutes). In this process, a neutron (in the U-239 atom) is transformed into a proton and an electron. The electron is immediately kicked out at high speed - as a beta particle. If you keep track of what's going on, you'll now see that what's left in the atom are ninety-three protons and 146 neutrons - presto - we've created neptunium-239 from our original uranium-238. And these atoms will eventually also be transformed by beta decay to plutonium-239. We can expand this idea to create any number of transuranic isotopes. For instance, if we added a couple more neutrons to the Pu-239, we get Pu-241. This isotope will decay into americium-241. One way to see how all this works is to study a copy of the Chart of the Nuclides. All of the known nuclides (about 2,000 of them) are grouped in the chart along with their properties.
Now, where do we find enough free neutrons to perform all those tricks we just did? Usually, in a nuclear reactor. Earlier, we said uranium and other heavy atoms were fissionable. This means they have the property that when they absorb a neutron, sometimes the result will be that the new nucleus breaks in two - or fissions. This fission event is very energetic (remember, there is a lot of force holding this nucleus together). So, the fragments go flying apart from each other with great force. If you can get lots of these atoms to fission, you can release a lot of energy (as heat). Now, the stroke of luck that allows this to happen is that each time a fission event occurs, several neutrons are also released from the atom. So, one fission event can provide the free neutrons needed to cause two or three more fission events. If we design our reactor correctly (the right materials, size, shape, amount of fuel, etc.) we can have plenty of neutrons available to make the fission process self-sustaining - and have plenty of them left over to be absorbed by other atoms - to produce transuranics, for example. The isotope U-235 makes a very good fuel for fission. But remember, most uranium is U-238. So, if we fuel a reactor with a combination of U-235 and U-238, we have both the fission fuel and the target for making transuranics. And once we let the fission process begin, we have the neutrons necessary to make both things happen.
For links on nuclear energy, radioactivity, or radiation protection, see the Radiation Information Network.
Keith Welch, Radialogical Controls Group (Other answers by Keith Welch)