Fins and Scales - Fish which have fins and scales are kosher. Fish which only have fins are not kosher.
Of the four types of scales, clenoid, cycloid, ganoid and placoid, only clenoid and cycloid scales are valid according to the Torah. Gandoid is the type found on sturgeon and placoid is found on shark.
The scales must be true scales that can be removed without damaging the skin of the fish. As it says in the Torah "These you may eat of the fish, all that have fins and scales..." Bony tubercles and plate or thorn like scales that can be removed only by removing part of the skin are not considered scales in this context.
Some fish that have such scales, such as eels, lumpfish, shark, sturgeon, and swordfish, are not kosher.
Shellfish, Mammals & Eggs - All shellfish and mammals (such as whales, and dolphins) are not kosher.
Only the eggs of kosher fish, such as fish roe or caviar, are allowed, therefore supervision is necessary.
Fresh and Filleted - Care must be taken when buying fresh, whole fish, filleted, or frozen, because of the possibility of substitution of non-kosher fish or of contamination by remnants of non-kosher fish from
knives and cutting boards.
Fish Sticks - Fish sticks may have three problems: the fish, the oil, and the frying utensils and equipment (which is usually used for non-kosher fish as well as kosher fish).
Blood - There is no prohibition against eating fish blood, other than the fact that people may think that a
person is eating prohibited blood in which case a sign must be posted indicating that the blood is fish
blood. Ritual slaughter is not required.
For more about fish...
Check out the "On Kosher Fish - FAQ" in Kosher Articles!