Let us start from the beginning.
Elementary particles are quantum mechanical entities. They can be described with the quantum mechanical solutions of the appropriate equations for the set up under consideration with the constants taken from the boundary conditions of the problem. In this it is not different than the situation with classical mechanics problems. The difference is that it is not a deterministic solution, the square of the mathematical solution gives the probability of finding the system in a specific state if a measurement is done.
Thus a measurement means picking an instance from the probability distribution for the specific problem.
Take the double slit experiment. An electron is arriving at two slits. The quantum mechanical problem is set up by the position of the slits, the size of the slits and the fields defined at the edges of the slit. It will not be easy to write the exact equations, but the experiment picks by a measurement, the (x,y) of the electron at the screen at distance z.
At the top, the individual hits/measurements look random. At the bottom an interference pattern is observed. The interference pattern is the measurement of the wave function squared , and it displays the entanglement of the electron with the geometry and fields of the two slits.
Measurement is a single instance that contributes to the probability pattern. Entanglement is what is displayed after the fact , when many measurements are performed and the entanglement can be displayed.
Both depend on the functional form of the mathematical solutions of the specific equations. The measurement of the probability distribution displays the entanglement in this example. If one has a clean and clear mathematical solution then the probability distribution is known, and thus the entanglement of the system, i.e. the functional dependence of the wavefunction on the variables and the quantum numbers can be predicted.
Coordinates, as in the example above, are continuous and the entanglement contained in the wave function regarding them is not simple. Quantum numbers like spin are discontinuous, spin up or down, and the entanglement displays the necessity of the conservation of quantum numbers in a simple manner. That is the part where people try to use "entanglement" in practical applications, but my background does not extend to that. One thing I am sure of is that no information can be transferred by entanglement. The information should be already there in the knowledge of the mathematical form of the wavefunction, and the measurement by finding what one component is immediately knows the value for the entangled component by quantum number conservation.