To create an archival or giclee print, we should first think about what not to do. The greatest enemies of print longevity are sunlight and acidity.
To avoid acidity, you must use a high-quality print stock. This translates to acid-free media that will remain acid-free over time. As certain papers age, like generic office copy paper, they generate acid when exposed to sunlight and air.
Although most papers are made out of wood pulp, this is infact one of the worst materials for fine art printing. Cotton Rag paper however makes a fantastic printing stock.
Acid could also come from a cheap ink set—for giclee printing, your ink set should be chemically neutral, which is rarely standard for a home printer.
With these specifications, your print will be archival. Taken care of properly, it will last for generations, which should be long enough to keep any customer happy.