True: " However, I can never find out exactly how two systems can be made to become entangled. Can anyone help me out with this problem. Thanks in advance for any help."
Roughly speaking, to make two systems entangled, you need to have interactions between them, such that one cannot distinguish the properties of any one of the two systems anymore in the properties of the entangled system. Think of a molecule, say the hydrogen molecule, H2. Quantum mechanically the behavior of the molecule is different from the behaviour of two individual atoms.
This is, in general terms, how you can see entanglement.
How can you practically make entangled systems? It depends. You can create a pair of entangled photons through a pair generation process, molecules you can create in the usual way (chemical reactions) or through forced collisions for odd and/or unstable compounds, and the list could go on and on and on.