That particles (quanta) are "located in several places at once" is a somewhat distorted view of modern quantum theory. Also there is no "Copenhagen interpretation" but several flavors of it. Even Heisenberg's and Bohr's version, who can be considered as the main "inventors" of the class of interpretations subsumed under "Copenhagen interpretation", differ. I'm myself a follower of the "minimal statistical interpretation", which is in my opinion also a kind within the Copenhagen family and the only one of all interpretations of the QT formalism I know so far which is strictly following the "no-nonsense approach" to physics, which means particularly not to make "esoteric" claims about the "meaning of the theory" but seeing it as a description of objectively observable facts about nature.
In this "minimal interpretation" the wave function (which makes sense only in the nonrelativistic limit; so I'll restrict myself to this limit, which however is already sufficient to understand an astoningishly wide range of phenomena in atomic and condensed-matter physics) describes the state of a single particle as a complex valued function ##\psi(t,\vec{x})##. This function must be square integrable, i.e., the integral
$$N=\int_{\mathbb{R}^3} \mathrm{d}^3 \vec{x} |\psi(t,\vec{x})|^2$$
should be finite. Then one can multiply the wave function by a factor (which is determined only up to a phase factor, which is however irrelevant for the physical meaning of the wave function) such that
$$N=1.$$
Then, according to Born (1926) the modulus squared of the wave function is the position probability density,
$$P_{\psi}(t,\vec{x})=|\psi(t,\vec{x})|^2.$$
I.e., the probability to find the particle in a small volume element ##\mathrm{d}^3 \vec{x}## around the location defined by ##\vec{x}## is ##P_{\psi}(t,\vec{x}) \mathrm{d}^3 \vec{x}##.
Now the wave function can be narrowly peaked around one position. One can prove that there exist such functions with a "width" as small as you want, but there is no state where the width vanishes. This would be a Dirac ##\delta## distribution, but that's not a state because it's not a square-integrable function (even the square itself doesn't make mathematical sense!).
This implies that a quantum particle can never have a precisely determined location. You can give the probability to find the particle in a certain region in space, but never a certain position! This doesn't mean that the particle is at many positions at the same time. Strictly speaking it's even weirder! The particle has no clear position at all although its position can be arbitrarily well determined, i.e., the probability to find it can be very large at some volume small on everyday scales and practically 0 everywhere else; then we say the particle is localized within an uncertainty that is small compared to macroscopic scales or the accuracy of a position measurement.
Further, the quantum mechanical formalism teaches us that not all observables can have sharply determined values. The most famous example, which lead to the Copenhagen interpretation and the idea of complementarity by Bohr are position and momentum. According to quantum theory, a quantum particle cannot have both a quite sharply defined value of the the ##x## component of the position vector and the ##x## component of the momentum vector, but the standard deviations of these quantities, defined with the probability distributions given by any "allowed", i.e., square integrable wave function must obey the famous Heisenberg-Robertson uncertainty relation,
$$\Delta x \Delta p_x \geq \hbar/2.$$
That means: If we have a well-localized particle its momentum distribution is pretty broad and vice versa.
