A related question was asked before: "Does functional programming replace GoF design patterns", with great responses.
The equivalent of "design patterns" is very vague in FP. In general, every time you see a "pattern" in your code you should create something to cover all of its uses in a uniform way. Often it will be a higher-order function.
For example, the following C code
for (int i = 0; i < n; i++)
if (a[i] == 42)
return true;
return false;
can be thought of some basic "design pattern" - checking if there's some special element on the list. This snippet could appear many times in code with different conditions. In FP, you simply use a higher order function several times. It's not a "pattern" anymore.
Functional programming has its own practices, but they are much different from "design patterns" in OOP. They include use of polymorphism, lists, higher-order functions, immutability/purity, laziness [not all are essential or specific to FP]... See also "what are core concepts of FP". Also, type classes (Haskell), modules and functors (OCaml), continuations, monads, zippers, finger trees, monoids, arrows, applicative functors, monad transformers, many purely functional data structures (book) etc. Functional pearls, already mentioned by Randall Schulz, form a very rich resource of FP at its best.
To learn how to write idiomatic code, any book/resource on a functional programming language will suffice IMHO (for example, RWH and LYAH); differences between thinking imperatively and functionally are always explained there.
In dynamic languages, Jeff Foster's link is a good collection; here is a very clever use of memoization in JavaScript that could be considered a "design pattern".