How do particles, such as electrons become visible? Quantum mechanics says that atoms are invisible - they do not have some specified location, only a probability distribution. So, how can we see them? If there is to be particle-antiparticle annihilation (or other interactions), the particles must have a fixed location, right? So, is this process just random? Is it impossible to know whether a pair will annihilate, but only know the probability?
 A: Firstly, let's address your statement that

Quantum mechanics says that atoms are invisible.

I would say that this is misleading at best.  Quantum mechanics says more something along the lines of "before we make a measurement of the position of a particle, we can only know the probability that if we were to make a measurement, then the particle would be in some localized region.  This is an example of what is called the Born Rule.  Once you make a measurement on the position of a particle, you can say with certainty that the particle is where you measured it to be, but you cannot have the same sort of certainty before the measurement is made.
When speaking of particle annihilation, we can certainly say that if we observed an annihilation to occur at a certain position, then the two particles that participated in the annihilation were both there during the annihilation event, even though we may have had only probabilistic information about their positions before the event.
Hope that helps!
Cheers!
A: I will continue where @joshphysics let off. You state:

So, how do they get visible? 

As he says, they get visible after the interaction.Here is an interaction of a photon entering a bubble chamber and becoming very  visible.

We experimentally   get the probability of interaction from knowing the flux of photons by the construction of the beam and measuring the number of times the interaction appears. The comparison of the theoretical calculations for the setup with the measured interaction probability ( cross section) validates the theory of probabilistic manifestation of quantum mechanical objects, in innumerable experiments.
The charged particles are visible because they ionize the medium, they leave a macroscopic trace, and the tracks turn because a magnetic field exists perpendicular to the photo, so we can get their momentum.

If there is to be annihilation with antiparticles, it must be "there", right? So, is this process just random? - we cannot know whether it will get annihilated - only we know probability?

We know the probability from the quantum mechanical solutions of the problem, yes, only the probability. Whether the specific electron ( or photon in the picture) will interact is a matter of the probability distribution for the given problem. Once the interaction  happens, it is very visible.
