With the shoe on, simply pull the elastic up over the shoe so it completely covers the laces. It makes it impossible for the shoe to come loose. The dancers in LOTD use this method. If you're still confused, ask your teacher or a friend who wears elastics for help. Shamrocks are the most popular and, I think, the prettiest.
Buckles are useful for catching the adjudicator's attention at feiseanna.
These are available at Antonio Pacelli for just a bit extra. You can also see them advertised as boy's soft shoes. They don't need the same amount of breaking in as heavies do as they are supplied fairly flexible.