How do you explain partial charges in molecules that have a dipole?
At some time the electrons will be at the fluorine end more often as it has higher electronegativity and thus making the hydrogen end partly positive. How does this work?

This is the charge distribution on the &quot;surface&quot; of the HF molecule, estimated by the program molcalc.org:

In a thought experiment, if you placed a negative sample charge (ideally with less charge than the elementary charge of the electron to not mess with the electron distribution) on the surface of the molecule, it would feel a force that is color coded in the picture (blue and cyan - attractive, red and yellow - repulsive). If you go sufficiently far away, the sample charge would not have any interaction because the molecule is net neutral. On the other hand, if you approach either nucleus, the sample charge would experience strong attraction (so the fluorine nucleus is not negative, even though we correctly assign the fluorine atom a negative partial charge).
To get a quantitative measure of the partial charge, you have to divide the space into two parts - that &quot;belonging&quot; to fluorine and that &quot;belonging&quot; to hydrogen. Then, you can sum up the charges due to the electrons and compare it to the nuclear charge.

If one electron is pulled to the fluorine end (the one that is shared), doesn't this just revert the hydrogen to its neutral state (as an element) and not be a partly positive charge?

Two electrons are shared. If you start with atoms, electron density from both atoms moves toward the center of the bond (very little, surprisingly, and drawing a stick for a bond is not very realistic but is great for counting electrons).
Your idea is that one electron is pulled to the fluorine. This is a very simple model, but let's explore it a bit. In this picture, the electron &quot;originating from the hydrogen&quot; would still be involved in binding, so we are not back to atoms.
What really happens is that instead of being spherically distributed around atoms, the electron distribution changes a bit when the bond is formed, with the bonding orbital (in the simplest valence bond or molecular orbital model) having electrons occupy the space near either nucleus, but not in a symmetric way. That leads to the charge separation.

Or does the electrons that are shared also including the lone pairs are going to orbit the shell of the other covalently bonded element, so that in some time there won't be any electrons in one end?

I did not understand this scenario. Maybe edit the question to clarify before it gets closed.