Ear piercings on the lobe of the ear take about 4-6 weeks to close, on average. This is the amount it would take any hole on the earlobe to heal. This assumes that no earring is kept in the ear at any point in time, which would inhibit the closing or healing process.
The healing process for other parts of the ear can be longer. A piercing on ear cartilage can take 3-6 months to heal. It's important to continually keep the hole clean, even as it is closing up. It's fairly common for pierced ears to become infected, but this is especially problematic if the swelling and redness spread beyond the hole.