The "scripting language" ("expression evaluator" would be more accurate) is a little stack-based intepreter that looks at lot like Forth.
So, for example, here's an example of a GENERATED coin getting spent:
TxIn: 73:3046...0f01
Prev.TxOut: 65:046d...bb9c CHECKSIG
That's intepreted as:
PUSH a 73 byte value onto the stack
PUSH a 65 byte value onto the stack
call CHECKSIG. CHECKSIG pops two values off the stack (public key and digital signature), then does the digital signature thing using the OpenSSL ECDSA_Verify() function.