Ions and Ionic Bonds I've recently just started learning about Chemistry, and more specifically, Ions.

In class, we learned about how Valence Electrons are electrons located in the outer-most orbitals and how every atom (with the exception of Hydrogen and Helium), want $8$ valence electrons.

When possible, an atom will attempt to get rid, or add, an electron to get $8$ on its outermost shells. For example, Sodium and Chlorine.

We learned that it's easier for Sodium ($\ce{Na}$) to lose an electron to get the $8$ outer electrons it always wanted, and for Chlorine to receive that $1$ refuted electron. Then, they form an Ionic bond and you get Table salt!

But now, I'm wondering: what if that's not possible? What if you have an element such as Beryllium and Lithium? Would they simply not combine? Or would something else happen? I am confused.
The variation from ionic to covalent to metallic bonding is not clear-cut, but a matter of degree. For example, the bond between hydrogen and oxygen in water is mostly covalent (sharing electrons), but at room temperature, about one in 10,000,000 bonds break, with the hydrogen losing an electron to oxygen -- the ionic bond you discussed.

However, in the case lithium and beryllium, there is not enough difference between them to favor one getting an electron instead of the other. However, something more interesting happens: both are willing to let electrons go, so there is a sea of electrons, unattached to a particular atom! This is called a metallic bond, and it enables many metals to mingle to form alloys, such as bronze, amalgams and stainless steel.