First you have to figure out how many outer (Valence) electrons each atom has.

Then, what the effective nuclear charge holding those electrons is.

Example: 3.16 (a) Lithium has the configuration 1s² 2s¹. The two 1s electrons are core and the 2s electron is outer or valence.  It is held by an effective nuclear charge of +1.  This electron is easily taken by other atoms that have a larger effective nuclear charge.
 

How do you know which are valence electrons and which are core electrons?  Only the electrons in the orbitals with the highest orbital number (Ex: 1s, 2p, etc.) are outer or "valence" electrons. ALL the rest are core. The valence electrons are farthest from the nucleus and are held the least tightly.  The core are close to the nucleus and held so tightly they "never" leave, at least not in ordinary chemical reactions.

Example: for  K (Potassium) the configuration is: 1s²2s²2p⁶3s²3p⁶4s¹
-- so only the 4s electron is outer. All the rest are core.
Another example: for  Se (Selenium) the configuration is: 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁴
-- so for Se, it is the 4s² and 4p⁴ electrons are valence and there are 6 of them. All the rest are core.

General rule 1:
1. When the effective nuclear charge is small (+1, +2, or +3), the atom will not be able to hold its valence electron(s) tightly. It will tend to lose them.

General rule 2:

2. When the effective nuclear charge is high (+7, +6, or +5) - the atom will be able to take  electrons from other atoms, and of course, it keeps the electrons it already has.

Basic principle:
Electrons want to be in the lowest possible state, even if it means switching atoms!

Applying this principle to the elements in the Second Row of the Periodic Table:
 

Element	Lithium	Beryllium	Boron	Carbon	Nitrogen	Oxygen	Fluorine	Neon
Configuration:	1s22s1	1s22s2	1s22s22p1	1s22s22p2	1s22s22p3	1s22s22p4	1s22s22p5	1s22s22p6
# of Valence electrons	One	Two	Three	Four	Five	Six	Seven	Eight
Effective Nuclear Charge	+1	+2	+3	+4	+5	+6	+7	+8
What it does:	Loses 1 e-	Loses  2 e-	Shares 3 e-	Shares 4 e-	Gains  3 e-	Gains  2 e-	Gains  1 e-	Full Shell --No Change
Resulting stable ion	Li1+	Be2+			N3-	O2-	F1-

Remember -- the number of protons (each having 1+ charge) does not change!! Only the number of electrons (each having 1- charge). The net charge is the difference.
-If you have more protons than electrons, the ion is positive.
-If you have more electrons than protons, the ion is negative.

Applying this principle to the elements in the Third Row of the Periodic Table:
 

Element	Na	Mg	Al	Silicon	Phosphorus	Sulfur	Chlorine	Argon
Configuration:	1s22s22p6 3s1	1s22s22p6 3s2	1s22s22p6 3s23p1	1s22s22p6 3s23p2	1s22s22p6 3s23p3	1s22s22p6 3s23p4	1s22s22p6 3s23p5	1s22s22p6 3s23p6
# of Valence electrons	One	Two	Three	Four	Five	Six	Seven	Eight
Effective Nuclear Charge	+1	+2	+3	+4	+5	+6	+7	+8
What it does:	Loses 1 e-	Loses  2 e-	Loses  3 e-	Shares  4 e-	Gains  3 e-	Gains  2 e-	Gains  1 e-	Full Shell --No Change
Resulting stable ion	Na1+	Mg2+	Al3+	Shares  4 e-	P3-	O2-	Cl1-	Argon does not for ions

3.15 Ca loses 2 e- and becomes Ca²⁺

3.16 (a) Li loses 1 e- (b) Cl gains 1 e- (c) P gains 3 e- (d) Al loses 3 e- (e) Sr loses 2 e- (f) S gains 2 e- (g) Si shares 4 e- (h) O gains 2 e-

3.17 see book

3.18 (a) stable (b) not stable (c) stable (d) stable (e) not stable (f) not stable (g) not stable (h) not stable (i) not stable (j) not stable (k) not stable (l) stable

3.19 (a) Li tends to lose one electron rather than gain one electron.  It only has an effective nuclear charge of +1.