In considering the periodic table, one should begin by noting that there are two large distinctions. Roughly the right 1/3 of the elements are non-metals and the left 2/3 are metals with a small number of semi-metals separating them.
All metals have certain common properties: they can be polished to a shiny luster, the conduct heat and electricity, are malleable and ductile, and in terms of chemical reactions, they will lose electrons to form cations (positive ions). The relative reactivity of metals depends on their ionization energy which determines how easy it is to remove the electrons from their valence shell. For alkali metals, there is one valence electron which is alone in a new energy level and consequently is easily removed. This causes that family of elements to be highly reactive and one never finds them in their pure form in nature. Alkaline Earth metals are in the second family which means they have two electrons in their valence level this gives them higher ionization energy and consequently they do not react as readily as alkali metals. Transition elements, because their outermost electrons are in s, p, and d orbitals, tend to be more stable and less chemically reactive than the previous groups. Also, because the orbitals overlap at these energy levels there are multiple electrons that can be removed to create ions with varying ion charge.
Nonmetals, on the other hand, do not lose electrons when they chemically react but are more likely to absorb an electron when exposed to a metal, or share electrons when reacting with other nonmetals. Consequently they will form negative ions (anions) when they react with metals.
In the case of representative metals and non-metals, they will react in such a way as to have a total of 8 electrons in their valence shell--metals by losing the electrons above 8, and non-metals gaining electrons to get up to eight. That is to say, the react in order to be isoelectronic with a noble gas as this is the most stable electron configuration. Even non-metals sharing electrons with other non-metals do so in such a way as to have noble gas electron configurations.
With this in mind, Alkali metals will react with fluorine in a one to one ratio of positive and negative ions (eg: NaF); Alkaline Earth Metals will react with fluorine in a one to two ratio of ions (eg: CaF2); halogens will each share one electron with fluorine (eg: FCl); transition elements will have varying ion configurations depending on the ionization number of the metal (eg: iron could be FeF2 or FeF3).
Noble gases have the best, most stable electron configuration. Consequently they do not normally participate in chemical reactions with any other elements.