I spent a couple of years working in the Astrophysics and Space Physics Section of JPL. Working with the Space Physics folks taught me a lot about the solar wind and other space weather phenomena. Later on, working with Hank Garrett of JPL's Space Environments group taught me more, especially concerning effects on spacecraft.
I'll start out with a description of what is a CME.
A big, fast coronal mass ejection (CME) (also here) is not all that different from the regular solar wind, except that: it is more localized; it moves a lot faster away from the sun; and the entrained magnetic field can be very different, especially in direction, from that of the solar wind around the CME. A CME is a rapidly-moving blob of magnetoplasma: it is largely ionized hydrogen (just like the solar wind), so protons and electrons, with a sprinkling of heavier atoms, and it carries with it magnetic field that was entrained in the lower solar corona. Almost all the atoms are at least singly ionized; some of the heavier ones are multiply ionized.
Although the mechanism that generates the CME is largely irrelevant to this question I'll mention it. It has to do with the behavior of magnetic fields in the lower corona of the sun. The field lines get stretched, twisted, and "kinked", and just like stretching and kinking a rubber band, this stores energy in the field. Occasionally those fields snap to a lower-energy configuration (a process called magnetic reconnection) and the energy suddenly released powers the CME explosion.
NOTE: there is no net electric charge to a CME. It is electrically neutral. But it is a plasma, so all those charge carriers can move around, at least a little.
But only a little, at least for movements perpendicular to the mag field lines. The matter (ions and electrons) and mag field in the solar wind and in a CME are tied together, so large-scale relative motion of one with respect to the other is inhibited. If an ion or electron tries to move with respect to the local mag field, the Lorenz force, F = q (V X B), where q is the charge on the particle, V is the particle's velocity, B is the mag field strength and direction, and X is the vector cross product, makes the particle spiral around the local mag field lines. It has a tough time crossing a lot of those field lines, because it keeps getting turned back by that Lorentz force. Conversely, if the mag field tries to change (which moves the field lines) this sets up a relative V with respect to the charged particles, and they begin their gyrating. I know this sounds like magic, but the physics of the situation has those gyrating charged particles generate their own mag fields (current loops generate mag fields, per the Biot-Savart law) that resist the change in the magnetic field. So the particles and mag field are "joined at the hip"!
Things get interesting at shock waves. Fast CMEs move at 2,000-3,200 km/s, while the fastest normal solar wind is about 1,000 km/s. This difference in speed is far faster than the "magnetosonic" velocity, the speed at which waves travel in the mag-field-plus-ions soup. So a shock wave forms at the front of such a CME. Shock waves compress things. In the case of a CME shock front, it's compressing the magnetoplasma, so the particle density increases and the mag field strength increases, rapidly. In the solar wind in front of the shock the mag field can be in one direction, and just behind the shock it can be in a completely different direction. Turbulence behind the shock front lends chaos to this transition and compression, so the mag field can be all over the place, both in magnitude and direction.
I mentioned the particle density increasing. But it's still what we would consider a hard vacuum. The "blast wave", the sudden impulse of momentum due to impact of the particles in the wave, is insignificant in a CME at 1 AU kinds of distances from the sun. There's just not enough mass involved. But a proton going 3,000 km/s has a kinetic energy of ~4.7 X $10^{4}$ eV (electron volts), which qualifies as ionizing radiation.
And changing mag fields generate electric fields, per Maxwell's equations. Rapidly changing mag fields generate strong electric fields. You see this in some of the earthly effects of CMEs: blown power transformers, power grids brought down, etc. There are fascinating descriptions of the 1859 Carrington Event, the largest CME impact on record, setting fires in telegraph stations and electrically shocking (some severely) the operators.
Now, to the meat of the matter: effects on spacecraft.
These kinds of electromagnetic things can happen on spacecraft. Spacecraft are just full of conductors, in the electronics, in the power systems, even in the spacecraft structure. In the face of rapidly changing magnetic fields (remember the telegraph lines of 1859!), long conductors, especially ones that form loops (they don't have to be circular loops) can generate voltages larger than the spacecraft's electronics are designed for, and can cause latch-ups and other damage. Even smaller voltages, in data lines, can corrupt data being transmitted between spacecraft systems, causing various kinds of problems from corrupted commands or table entries (such as in star trackers) to operating system crashes.
The multi-kV radiation burst at the shock front can cause any of the problems associated with radiation at such energies, such as single-event upsets (SEUs) and bit-flips.
Most modern spacecraft are designed to handle these kinds of events, and those designs are generally successful. I'm not sure if their margins are large enough to handle another Carrington Event.
But there are some effects these designs can't handle, and those involve the wildly varying magnetic field, and heating of Earth's upper atmosphere. Many spacecraft operating within the lower parts of Earth's magnetosphere use magnetic torque rods, also called magnetorquers, for attitude control, since they require no propellant or moving parts, just electric power. They depend on Earth's magnetic field behaving "normally", i.e. predictably. When a CME hits Earth's magnetopause the magnetic chaos propagates into the magnetosphere and the usually-predictable mag field becomes quite unpredictable. Satellites with no secondary attitude control systems to back up magnetorquers will lose attitude control.
A fair fraction of the energy a CME delivers to Earth winds up in Earth's upper atmosphere, heating it. This makes the gas expand, so it moves outward, occupying more volume. This makes the average density go down. But spacecraft don't move outward with the atmosphere, they stay at their orbit altitude—for a while, anyway. At a given, fixed altitude, the heating causes the air density to increase, causing more drag and thus more energy loss and altitude loss. Dropping ~3 km in a day or so of a magnetic storm's duration is a lot.
I hope this is useful!