this doesn't often occur. The other party may not opt risk disregarding the award given. Simply because they are presumably entitled to pay all costs in the per-arbitration to ensure that they change the ruling and it also entails paying for the attorney's fee.
However, if it becomes indispensable, one may request the court in a summary motion to convert the award to a judgment. Hence enforcing it like any other court judgment. If it is local, it may be implemented and confirmed under that Province/State's arbitration act that's applicable. Additionally, if it is international, it may be confirmed and enforced in any of the 149 countries that are signatories of the New York Convention.
The whole process of confirming an award requires a judiciary. A summary proceeding that may or may not be inexpensive and quick. No trial is required nor is it a litigation.