I doubt they would pump water to the geothermal source to heat it.

How would it work?

Instead, water would likely be withdrawn from the heatsource with production well pump station. Do heated water wells exist around volcanos? Are they accessible with today's well drilling techniques? If not, perhaps they WOULD pump water to the source for heating. Is it saline water? The water should be filtered to keep the system clean. Active pumping and filtration would reduce the efficiently of the plant depending on the power required to produce and filter the water/steam. Once we have heated water/steam, they would be separated with the steam driving a turbine and hot water going through a series of heat exchangers and vaporizers to extract remaining steam to assist the turbine. Any liquid remaining would be used to help cool the process and be pumped back into a cooler region of the geothermal source with an injection well pump station.

What about seismic activity?

Construction means and methods (modern building code) have already been developed to allow for industrial facilities to endure major seismic events. Even with modern building codes it would be very challenging and risky to design a geothermal plant which is coupled to an active volcano. I suppose it may be possible to have a series of controlled eruptions to manage the risk.

Also consider that process critical instrumentation is usually sensitive and may become prone to failure if jarred frequently. When instruments don't work, the process cannot be automated and may need to shutdown. Redundant instruments can help combat this problem.

What to do with the heat you generate and/or don't use?

This is a big problem with power generation that usually decides where the plant is located. It is secondary to fuel storage, but this is a geothermal plant so fuel storage isn't necessary. To manage the heat, you need a system of large chillers, cooling stacks, and passive/active heat exchangers. For scale, consider a stand alone dump radiator such as a residential split system outdoor unit. Now consider the amount of heat your house generates compared to the amount the geothermal plant would. This adds drastically to costs because it also needs to be able to survive any seismic event and possibly an eruption. The plant footprint is getting larger and larger and residents don't like large industrial facilities in their backyards either.

What about the condenstation that results from cooling excess heat?

Something must be done with the condensation that is formed as a result of cooling, just like an indoor A/C unit needs to drain. This probably would need to be discharged to a body of water or added to the injection well. How close is the body of water? Is it protected? What type of permitting is required to discharge condensation from an industrial facility? Is there a fragile ecosystem? Maybe injection well is a better deal, although permitting is still likely required.

What happens to the plant if the volcano erupts?

It should be designed to withstand any eruptions short of a cataclysmic event. The plant should go into a controlled shutdown if a major seismic event occurs.

But what to do with the magma, if there is any? Is diverting feasible? How about the volcano ash that will accumulate on structures? They need to be designed for additional load so they do not collapse under the added weight (probably not symmetrically loaded, either).

Furthermore, the gases that are released by volcano eruptions are water vapor, carbon dioxide, and hydrogen sulfide (extremely corrosive). Now all outdoor equipment may need to be corrosion resistant, depending on exposure to H2S. H2S also explosive so we want to monitor H2S levels in confined spaces and at risk areas as well as install explosion proof equipment where needed.

Okay, we are generating electricity, now what?

Now sub stations and power transmission lines are needed to connect to the existing power distribution system. Where will the substations go? They should be near the plant which adds to the foot print. Furthermore, local utility generators are somewhere else which means the electrical system needs paralleling equipment with protective relaying which would match voltage and frequency of the grid. Now its time to coordinate the protection controls requirements with the local utility to ensure the systems play nicely. One system has to be the master. The protection systems should probably be redundant, too.

Source: Electrical, Instrumentation and Control Designer for Industrial Facilities.

TL;DR I got carried away. Geothermal power plants are cool. No pun intended.