I'm guessing they meant to pitch their yeast after brewing. That's a fairly long time to go without any yeast activity, but thankfully we know that the airlock isn't a reliable indicator of fermentation.
OP, take a peek inside the fermenter and see if there are any bubbles, or any foam on top. That would be Krausen and it would indicate that fermentation has commenced.
The lack of foam or bubbles *might* indicate that fermentation has not started. In this case you might take a sample (being very sanitary) and measure it with a hydrometer to see what the gravity is. Compare with the OG of the batch.
Check back here with the results. Yeast are not hard to get going as long as you don't expose them to too much heat (say wort that was above 100 degrees for Ale Yeast) and you give them something to eat, which would be the sweet wort. Generally as long as the temps are correct (for most ales in the low to mid 60's) they will do their thing.
I'd like to caution you about buckets. Although they can be a great choice for fermenting in, they always carry the risk of having small leaks around the lid, which isn't really a "risk" per se. It just means that bucket are less often apt to bubble through the airlock, as the CO2 gas can escape through the bad seal is all. It's not a problem.
If you are using a carboy of some sort and know you have a good seal on the airlock then not seeing any bubbles in the airlock *might* mean that fermentation is not happening, but you can usually just look in the carboy and see that it's not happening.
Also, you DID remember to fill the airlock with water, Starsan, or Vodka, up to the line, right?