They can be bought from Traders; the Karmarama offer the best deal; or harvested from Plants grown on the Bio deck in many climates. The Kasvagorians like to purchase them. If you have no Food Supplies at all, Arona Daal will have at least one crate available.
The best Bio deck environments to produce food crops are the Siren's home environment (High moisture, high temperature) and the Zedem Monk's home environment (Medium moisture, high temperature) as both plant types in these environments produce food crates.
Note: unlike other items, researchers will not automatically research improvements of Food supplies, they will only do so when provided with crates on the Analyser. As food supplies can not be manufactured, improvements have no effect, so this is only an issue if you want to fill out the research tree.