Here is an event with three electrons and two positrons in a bubble chamber picture.
A photon has come in from the left transferred a lot of its energy and momentum to an electron and a soft electron positron pair with the same vertex, and went along and created a second electron positron pair with higher energy, the electron ( possibly proton or nucleus) on which it interacted being a spectator and not visible in the chamber.
We know the position of the electron at the vertex with micron accuracy and its momentum from the curvature of the magnetic field with some measurement uncertainty. The delta(p)*delta(x) satisfied the HUP because h_bar is a very small number.
Were we able to measure the position with an accuracy of 10^-10meters we would be in the atomic world and the HUP would hold for the electron. with h_bar of the order of 6.5*10^_16eV*second we would still be ok with HUP for the momenta in these interactions.
The HUP is constraining when the orders of magnitude of x and p are both of atomic dimensions .
Do electrons just randomly teleport according to the probability distribution or do they actually travel in 'normal' trajectories (going step by step instead of teleporting, for example footballs travel in step by step and don't randomly teleport AFAIK)
When one is in the dimensions where quantum mechanical dynamics holds one cannot think of particles as billiard ball analogues or of waves as water wave analogues. These electrons we see in the picture are "entities" described by Quantum mechanical solutions to the dynamics of the problem that we identify macroscopically as "electrons", in dimensions where h_bar is to all intents and purposes of measurement zero.
The quantum mechanical solutions tell us that electrons , i.e. entities that we can kick off as we did in the picture, are in orbitals around the nucleus of the atom, and have very specific quantum numbers and quatized energy; and these quantum numbers come from the solutions of the QM equations of the problem, and they identify orbitals for the electrons. If the atom is undisturbed there is no way to identify the location of an electron entity except by the mathematical solutions to the problem.
The shapes of the first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz. The colors show the wave function phase. These are graphs of ψ(x, y, z) functions which depend on the coordinates of one electron.
That is all we know, the interaction crossection probabilities, as is the case in the picture. It has no meaning to ask about an exact position of an electron, because the QM entity that manifests as an electron macroscopically can only be localized by probability functions: what is the probability to find an electron at a specific (x,y,z) if probed with a photon, for example.
Quantum mechanics is deterministic, in the sense that the evolution of the probability distribution (i.e wave function) can be obtained rigorously by solving the Schrodinger Equation.
However, quantum mechanics is not "as deterministic as you would wish", in the sense that there is Heisenberg uncertainty principle. The uncertainty principle arises from the fundamental property that quantum observables do not always commute with each other, i.e. generally $\hat A\hat B\neq \hat B\hat A$, and as a result, if a quantum state has a definite value for $A$, it cannot at the same time have a definite value for $B$, and vise versa. This is in sharp contrast with the way we perceive the world works -- for example we say we know the state of a billiard ball only if we know both its position $x$ and its velocity $v$. Well quantum mechanics says this is simply impossible for quantum states (which means for all states in real life).
But things are not that bad. The uncertainty principle says that the uncertainties $\Delta A$ and $\Delta B$ satisfy $\Delta A\Delta B\sim \hbar$. You see that while it is impossible to be absolutely certain about both ($\Delta A$ and $\Delta B$ cannot both be zero), but you are still pretty certain, in the sense that the "average uncertainty" $\hbar$ is really really a small number.
Best Answer
A photon is a name given to a lump in an electromagnetic field that can cause a single electron to change from one energy level to another. The size of the lump in a given region tells you the probability that it will make an electron change its energy level. The first thing to note about such a lump is that it doesn't have a single location. Rather, it is spread over an extended region. Now, it can be the case that if you track the evolution of the field over time, a lump in some region R1 can give rise to another lump in some other region R2. But you can't pick a particular point x1 in R1 and say that the field at x1 gave rise to the field at a point x2 in R2. Rather, the lump in R1 gave rise to the lump in R2. If you change the shape of the lump in R1 away from x1 this will in general change the probability of observing something in a sub region of R2 around x2. So you can't say the photon travels along some trajectory from x1 to x2.
And what I have said above is only an approximation because in general you can't localise a field so that it only has a non-zero value in some bounded region. The best you can do is change the field so that you will have a higher probability of seeing a photon in some region.
The above discussion alone would mean that a photon doesn't have a trajectory, but in general the situation is even less trajectory friendly than that. Different photons with the same energy aren't distinguishable: all you can say is "there are so many lumps in the field in this region". If you have some region R3 at t2 and there are lumps in R1 and R2 at t1 both of which are within (t2-t1)/c of R3, then there is in general no fact of the matter about whether the lump at R3 corresponds to the lump at R1 or R2 since they both contribute to R3 and all you can measure is something like the number of lumps.
If you want to understand this issue properly you should read about quantum field theory. A good book about QFT is "Quantum field theory for the gifted amateur" by Lancaster and Blundell.
More explanation. The OP asks if the particle can be in two places at once. Suppose that the field in a particular region is such that you have a very high probability of only measuring one particle in some given period of time. In general you will not be able to explain the results of experiments in that region by saying the particle has gone down one particular trajectory. Changes in different places in that region will all change the final outcome of the experiment. You could say the particle is in more than one place at a time in that sense. The particle doesn't appear or disappear from one place or another in the region. Rather, the field changes gradually over time so that the particle changes its probability of being in different places.