How do I decide which element gets written first in a chemical formula?

There is a simple convention plus a balancing step. First, write the more electropositive element (usually the metal or the element further left in the periodic table) first, then the more electronegative one (usually the non-metal). For example, sodium before chlorine in NaCl. To get the subscripts, use the valencies and the criss-cross method: write each element's valency, then swap them to become the subscript of the other element. For aluminium (valency 3) and oxygen (valency 2), crossing over gives Al2O3. Finally, simplify the subscripts to the smallest whole-number ratio if needed, for example Mg2O2 becomes MgO. For polyatomic ions like sulphate, keep the group in brackets when more than one is needed, as in Al2(SO4)3. So: positive element first, criss-cross the valencies, then simplify.