That, of course, depends on which "supplement" you are lacking.
The commonest cause of anaemia is iron-deficiency anaemia. Taking a typical dose (roughly 150-200 mg of elemental iron per day in divided doses) usually allows your haemoglobin to increase by 1.5-2 g/dl every three weeks.
However, iron therapy's job doesn't stop once your haemoglobin is back to normal. What you also need is to replenish the body's stores of iron. Therefore, it is recommended that treatment lasts for between three and six months at least. Compliance is an issue here, though, since iron tablets can irritate the gastrointestinal tract in a certain number of cases (there are a few tricks you can try for this though).
If your anaemia is secondary to folate deficiency, it is recommended that you take folate supplements for around 4 months. The reasoning is much the same for iron, but folate tablets are much easier to tolerate for most people.
Lastly, vitamin B12 deficiency anaemia is usually treated with six (1000 µg) intramuscular injections at three to seven day intervals (often weekly injections, or two injections per week, are organised, as they are easier to remember). This is enough to fill up even the most B12 deficient individual, but has the disadvantage that it is, of course, injected - an idea to which some people are quite resistant. There are tablet forms of vitamin B12, but the problem is that, unlike iron and folate deficiency states, people who are deficienct in B12 usually have some problem with the absorption of the vitamin from the gastrointestinal tract. If this is the case it obviously won't help to give B12 tablets, and so it has to be given some other way/ Sadly, that requires an injection.