In ionic bonding between atoms, one atom takes an electron from the other and becomes negative, while its partner becomes positive. The two atoms are then held together by their opposite charges. In contrast, with a covalent bond two atoms share a pair of electrons. However, if one atom has a greater pull on those electrons -- a property known as electronegativity-- it will become partly negative and the bond is said to be partly ionic. You can calculate the percentage of ionic character of a bond by considering the difference between the electronegativity values of the two atoms on either side.
Look up the electronegativity values for the elements which have the two adjacent atoms sharing the bond. You can generally find values of electronegativity on periodic tables or charts given in standard chemistry textbooks and reference books. For example, if you were considering the compound hydrobromic acid (HBr), you would look up the electronegativity value for hydrogen (H is 2.1) and bromine (Br is 2.8).
Subtract the lower electronegativity value from the higher to find the difference between the two. In the case of HBr, the difference is 2.8 - 2.1 = 0.7.
Calculate the ionic character of the bond between the two atoms according to the following formula: 1 - e^[(-0.25)(X^2)], where "X" is the difference in electronegativity that you just found. The term "e" in this equation is a mathematical constant known as Euler's number and most scientific calculators will include this function. In the example of HBr, the calculation would be as follows: 1 - e^[(-0.25)(0.7^2)] \= 1 - e^(-0.1225) \= 1 - 0.88 \= 0.12
Multiply value you calculated by 100 to obtain the percentage of ionic character of the bond. The percentage of ionic character of the bond between the two atoms of HBr is 100 x 0.12 = 12 percent.
TL;DR (Too Long; Didn't Read)
Electronegativity of elements increases going up and to the right in the periodic table, with fluorine having the highest value.