By capturing neutrons (which, not being charged, escape the magnetic confinement continuously as the reaction goes on) with a moderator blanket which is then cooled with water/steam.
How to keep the blanket from quickly degrading and becoming nuclear waste seems to be an open problem (not too different from what goes on in fission reactors though)
> How to keep the blanket from quickly degrading and becoming nuclear waste seems to be an open problem
Not really. Most reactors plan to also use the neutrons to breed the tritium fuel for the reactor, so the blanket would consist of liquid metallic lithium. The only products from neutrons reacting with lithium nucleii (either 6 or 7) are He-4 and tritium.
The open problem is how to safely maintain the reactor-facing wall of the lithium blanket. It gets bombarded by a lot of neutrons, yet needs to contain the hot lithium. It helps that the lithium can be unpressurized, but it's still a problem, because molten metallic lithium is not fun to have leak into anywhere.
The plan of the ARC guys appears to be to design the reactor so that the lithium vessel is easy to remove and swap for a new one, and just use steel for the vessel. The downside of this is that it's going to result in a lot of low-activity waste -- actually probably quite a bit more than what fission plants produce. There are other approaches, including using a material that doesn't really get activated by neutrons, and which is maintained above it's annealing temperature so embrittlement caused by dislocations is repaired as it happens. The downside of this is that materials above their annealing temperatures can be kind of soft.
By the way, this type of reactor is technically a hybrid fusion-fission reactor. Because when the neutron hits a Lithium-6, what happens is a fission reaction. Lithium-6 absorbs the neutron, and then splits (in Tritium and Helium) and releases energy. We are taught that fission happens only for heavy nuclei, and this is mostly true, but Lithium-6 is an exception. The energy released in the fission of Lithium-6 is quite comparable to the energy releases in the fission of Uranium or Plutonium (4.8 MeV for the fission of one Li-6 nucleus vs about 200 MeV for Uranium-235 or Plutonium-239; that energy is nearly perfectly proportional to the atomic mass).
It looks like all the isotopes of LI are very short lived. Is the problem some of the daughters, or perhaps the Fe and C in the steel that are the problem?
Unpleasantly, molten lithium metal corrodes steel. Glass, too.
Making the blanket out of molten metal would be a problem anyway because it is conductive, and you are trying to control a magnetic field inside the reactor chamber with coils around the outside of the blanket. Varying magnetic fields would set up eddy currents in the metal that would oppose changes to the field. So you probably need a diamagnetic insulating compound of lithium. What to bind to the lithium is a tricky question, because you don't want it stealing neutrons you need to breed tritium from, and getting radioactivated besides.
Under ideal conditions, if you had pure 6Li and 7Li, a neutron it stops would end up producing more than one tritium nucleus. The problem is that you have a great deal of other stuff that will steal neutrons, including pipes.
You could make the blanket with LiD, lithium deuteride, and any neutrons the deuterium picked up would make a tritium. But lithium deuteride melts up around 700C, which is hotter than most people like to imagine operating reactors. Worse, you cannot chemically distinguish the deuterium from the tritium, when you try to extract it.
There is a separate problem of extracting any bred tritium, in parts-per-billion concentration, out of the blanket.
How to extract bred tritium at parts-per-billion concentration from hundreds or thousands of tons of "blanket" material quickly enough to cycle back into the plasma has not been studied, and might not be possible.
Furthermore, nobody knows how to get enough tritium bred in it in the first place. You need for each neutron captured to breed more than one tritium nucleus, to make up for the fraction that fails to breed any. A fusion reactor with no fuel is a remarkably expensive doorstop.
It's too bad no one's figured out a way to capture the output of a nuclear reaction and convert it directly to electricity without the intermediate heat cycle. Instead, most of the energy generated is just waste heat, and only a fraction of the energy generated is used for something useful.
How to keep the blanket from quickly degrading and becoming nuclear waste seems to be an open problem (not too different from what goes on in fission reactors though)
https://en.wikipedia.org/wiki/Fusion_power#Energy_capture