All 3 words can be said to be "prescriptions" in English, but ...
a "recept" (literally "recipe") is written order to a pharmacy for a specific drug or medication. A doctor give you a slip that specifies that you are entitled to purchase 300 tablets of 100 mg substance.
"förskrivning" in this case could be said to be the same thing, it just has another root, as it literally means "to write for", so is based on the verb "to write", while "recept" is based on the noun "recipe" (the same as recipies for food).
An "ordination" is more general medical order, a recept is by its nature an ordination, but an ordination does not necessarily have to be a "recept". An example that clarifies the difference would be an "ordination" to walk at least half an hour each day, that would not be on a receipt. While a certain amount of morphine to be gotten from a pharmacy would be both a "recept" and an "ordination".

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Note added at 20 mins (2017-10-24 19:35:59 GMT)
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you can also see it in terms of generalizations,
"recept" is very specifically a written order to a pharmacy for drugs.
"förskrivning" is a more general written medical order of some kind.
"ordination" is the most general, and can even be used without explicitly referring to something given in writing.