Just walk around a lot. It's about the same answer as the first one, but I'll be more specific here.
If there are two Pokemon that can breed in the daycare at that moment, every 256 steps you take, the game will roll for a value, and if that value falls into a specific range, an egg will be created for you to pick up. More information about the values can be found here.
As for how long it'll take to hatch the egg, it will take 3,840 steps, or 15 egg cycles. That information was found on the Spearow/Fearow dex page, under egg cycles.
Source: the above link