Assuming "+ private key (32 bytes) +" stands for the private exponent of the key, you have to prepend the version byte 0x80, then apply Base58Check (see the "Encoding a private key" section of https://en.bitcoin.it/wiki/Base58Check_encoding )

Edit: Actually the whole process is outlined step-by-step at https://en.bitcoin.it/wiki/Wallet_import_format