Functions in PL/Python are declared via the standard CREATE FUNCTION syntax:

CREATE FUNCTION funcname (argument-list)
  RETURNS return-type
AS $$
  # PL/Python function body
$$ LANGUAGE plpythonu;

The body of a function is simply a Python script. When the function is called, its arguments are passed as elements of the list args; named arguments are also passed as ordinary variables to the Python script. Use of named arguments is usually more readable. The result is returned from the Python code in the usual way, with return or yield (in case of a result-set statement). If you do not provide a return value, Python returns the default None. PL/Python translates Python's None into the SQL null value.

For example, a function to return the greater of two integers can be defined as:

CREATE FUNCTION pymax (a integer, b integer)
  RETURNS integer
AS $$
  if a > b:
    return a
  return b
$$ LANGUAGE plpythonu;

The Python code that is given as the body of the function definition is transformed into a Python function. For example, the above results in:

def __plpython_procedure_pymax_23456():
  if a > b:
    return a
  return b

assuming that 23456 is the OID assigned to the function by PostgreSQL.

The arguments are set as global variables. Because of the scoping rules of Python, this has the subtle consequence that an argument variable cannot be reassigned inside the function to the value of an expression that involves the variable name itself, unless the variable is redeclared as global in the block. For example, the following won't work:

CREATE FUNCTION pystrip(x text)
  RETURNS text
AS $$
  x = x.strip()  # error
  return x
$$ LANGUAGE plpythonu;

because assigning to x makes x a local variable for the entire block, and so the x on the right-hand side of the assignment refers to a not-yet-assigned local variable x, not the PL/Python function parameter. Using the global statement, this can be made to work:

CREATE FUNCTION pystrip(x text)
  RETURNS text
AS $$
  global x
  x = x.strip()  # ok now
  return x
$$ LANGUAGE plpythonu;

But it is advisable not to rely on this implementation detail of PL/Python. It is better to treat the function parameters as read-only.