If you read the literature on fusion rockets you probably have a pretty firm idea in mind of what they're good for and when they'll be relevant - in "the future". No good fusion rocket paper is complete without a superconducting magnet here, and a magnetic nozzle there - in fact, these widgets are a primary ingredient of any fusion propulsion design and the more infeasible or untested they are, the better. This seems obvious: fusion rockets are the future because we don't have fusion yet.. right? Actually, no.
Producing nuclear fusion isn't all that hard. Amateurs regularly cobble together desktop fusion devices like the Farnsworth Fusor and other contraptions. The significant hard problem of fusion is getting more energy out of the device than you put into it. The current government backed effort to achieve this is the ITER project who are building a tokamak style device, but many other schemes are also being tried, with significantly less funding.
One of these is the dense plasma focus of hydrogen/boron fuel, a combination called focus fusion. The technique is relatively easy to understand. You take a metal chamber and put a single tubular electrode in the middle, ringed by a number of solid electrodes. Pump all the air out with a vacuum pump and then add the fuel until it is at a few torr. Dumping about two mega-amps of current into electrodes causes a plasma compression called the "pinch" in which nuclear fusion occurs. The result is a stream of electrons in one direction, a stream of ions in the other direction and a whole lot of x-rays, and virtually no neutrons. These happen to be the perfect products for producing electricity and if that's your goal, it means you can do it very efficiently.
The challenge of focus fusion is getting enough power into the device to burn the fuel - typically done with a big heavy bank of capacitors - and containing that heat in the plasma for long enough. Hydrogen / Boron 11 (or pB11 as it is often called) is the hardest fuel to get fusion going, requiring temperatures over 123 keV. As such, dense plasma focus fusion researchers tend to use deuterium instead, which only requires temperatures of 15 keV. The government program uses deuterium/tritium which only requires 13.6 keV, but tritium is a little hard to come by - it has to be made in nuclear reactors - and is strictly controlled. Deuterium can be picked up in rented bottles from your local gas supplier.
Using a dense plasma focus device to produce deuterium-deuterium fusion is pretty simple and requires minimal startup costs - especially if you do your homework and learn from the mistakes of others. Unlike pB11 fuel, D-D fusion produces neutrons. Shielding fusion researchers from neutron exposure is easily achieved with two things: distance and concrete. Measuring neutron output can be as low tech as looking for bubbles in a contained gel, and as high tech as CCD detection of scintillator stimulation. When you're producing neutrons you know you're achieving fusion.
Getting back to rockets, let's look back up at how I finished my first paragraph describing focus fusion: producing electricity [..] if that's your goal. While nuclear-electric propulsion sure is sexy, what if our goal is just to make a good old nuclear thermal rocket? Back in the 60s the US did a lot of great nuclear-thermal rocket work. They were using highly enriched uranium folded into a solid core with liquid hydrogen running through it. They got specific impulse in the 850 s (vac) range and had plans to achieve higher power before being defunded for obvious political reasons. So what might a nuclear fusion thermal rocket look like?
As our goal is to produce heat, not electricity, it makes more sense to use deuterium as our fuel. We only need to produce pulses of electricity to feed into the electrodes to produce fusion, and the most readily available technology to do that with sufficient power density is a compulsator. Much like an alternator, a compulsator is an electromechanical device that converts mechanical rotation to electrical energy in the form of alternating current. A high power rectifying bridge converts that to direct current to feed into the dense plasma focus. Compulsators have been built for railguns which produce more than enough current (and way more than enough voltage). I haven't read much on reducing pulse width (sometimes called "rise rate") of compulsators, but the ~2 microsecond pulses needed for dense plasma focus does seem challenging.
The rest of the rocket cycle is pretty standard. The expansion nozzle is cooled by cycling the fuel through it, this heats the fuel enough for a state change to occur and the expansion is used to turn a turbine which pumps the fuel, and finally the fuel is used to cool the core. The only difference is that the turbine serves double duty by turning the compulsator. A smart engineer will recognize that the rotors of the compulsator could be the turbine. Similarly, although all three components are shown schematically as being on the same drive, there most likely will be gearing involved to keep the pump constant.
Unlike a device for the production of electricity, the dense plasma focus will probably be made from copper. This will absorb the x-rays and transfer the heat to the "fuel" (aka, the coolant, traditionally the propellant-which-isn't-an-oxidizer of a rocket has been called the fuel). The already slow neutrons will pass right through the copper core and be slowed more by the fuel, hopefully enough that they don't hit the outer chamber with enough velocity to make it irradiated or contribute to wear.
Speaking of fuel, most readers familiar with nuclear thermal rockets have probably been thinking about hydrogen this whole time. Although compulsators are certainly more mass efficient than equivalent capacitors and the means to recharge them, they are not known for being light. As a fusion rocket is incapable of spreading radioactive material into the atmosphere, the traditional safety concerns of launching nuclear thermal rockets from the ground does not apply. As such, propellant density is once again important and a hydrocarbon first stage fusion rocket doesn't need strap-on boosters trumping its inherent safety.