None of these other answers are fully correct so I thought I should add my own.
Whether or not an egg is produced is decided ever 256 steps you take, so if you're standing still, nothing will happen. You can't just wait. Whether or not an egg is produced is based on how well the Pokemon in the Daycare are. A detailed list of what the Daycare man/lad/lady say about your Pokemon that can help you determine this chance can be found in my source below. Aside from what is said about your Pokemon, the chance an egg has to appear every 256 steps can be determined by what two Pokemon are being bred:
- If the Pokemon are the same species and have different OTs, the chance is 70% (88% with the Oval Charm)
- If the Pokemon are the same species and have matching OTs, the chance is 50% (80% with the Oval Charm)
- If the Pokemon are different species and have different OTs, the chance is 50% (80% with the Oval Charm)
- If the Pokemon are different species and have matching OTs, the chance is 20% (40% with the Oval Charm)
It should also be noted that these percentages are different in Generation II. The circumstances and correlating percentages for these games can be found in my source below.
Source