It depends on many things. One is your age, the other is how advanced is your anemia, the third is the type of treatment you get.
A child will recover fairly quickly compared to an adult. My son was once found anemic and was prescribed medication (iron supplement vitamins) and he was almost completely recovered by one week.
An older person would perhaps take longer to recover, anywhere from 2-4 weeks, with an iron supplement. There's more information in this page.