Once an entangled particle is measured, it's wave function collapses. From my understanding, any sort of information exchanged to the particles can be considered a mistaken measurement. So how do researchers entangle particles, move them apart and then measure them? I assume they are held in vacuum and are maintained within a specified volume of space through magnetic confinement, but I would think that the magnetic fields holding them would also consequentially be a measurement on them. So I am at a loss as how they keep them entangled until an actual measurement is performed. I assume it's because my understanding of what is considered a measurement is flawed since I've read that even energy can be delivered to entangled particles even without collapsing their wave functions.
When experiments are performed on entangled pairs: Photons are the most common choices for entangling quanta, and Bell tests are common uses of entangled pairs. Generally, the entangled photons are NOT stored at all. Upon creation, they are routed to detectors for measurement on the desired basis (polarization/spin is common, but there are also many other bases). Usually there will be a lens of some type to collect the photons, and then focus them towards their respective detector apparati.
They may be routed through the open air or through fiber without much loss in fidelity (i.e. without unintended decoherence/collapse*). For example, open air Bell tests have been performed across distances of 144 kilometers and greater. Fiber has been used for 100 kilomters. Photons may also have certain operations performed on them which will not cause collapse: filtering at a specific wavelength, applying half/quarter wave plates, refection via mirrors, certain types of lenses or splitters, etc. Here are references of some experiments, which describe their specific setups:
Other particle types will have different requirements to insure that there is no loss of entanglement prior to when measurements are taken. There may be temporary storage. And temperature (thermal effects) may be a consideration, with cooling necessary. There are a lot of types of quantum objects that can be entangled. Here is a Bell test using entanglement of electron holes:
*Using the common meaning of "collapse" in the literature.