How do you balance these two chemical equations?

In order to balance both of the reactions you need to make sure that both sides of the reaction have the same number of atoms for each atom in order to follow conservation of mass.

KCl+F₂→KF+Cl₂
Notice how in the above reaction there are two chlorine atoms on the products side (right side) and only one atom of chlorine on the reactants side (left side).  you want both the reactants and products side to have the same amount chlorine and to do this multiply KCl by 2.  Fluorine however, has 2 atoms on the reactant side and 1 atom on the product side.  to fix this multiply KF by 2. Therefore the balanced reaction is: 2KCl+F₂→2KF+Cl₂
notice how both sides of the reaction have equal numbers of each atom.

Mg+HCl→MgCl₂+H₂
the above reaction has 2 atoms of H on the products side and only 1 atom of H on the reactants side.  That means you have to multiply HCl by 2.  Now you have the equation Mg+2HCl→MgCl₂+H₂. As you can see now we have equal numbers of all the atoms on both sides which means that that is the balanced equation.

I hope this helps.  Let me know if you have any further questions or need anything to be clarified.

Ions gain or lose electrons