You can also try to get the key by running a rainbow table attack as well.
The problem as far as I know is that you cannot get the key if the password isn´t listed in the actually dictonary file or the wordlist.
There are several such wordlist, dictonary list, wpa tables out there, some up to 30GB in size.
A bruteforce attack may take days or weeks to complete and further more not sure if even then it can crack a 128bit cryption.
I would love to see a solution to this as one of my previous attempt failed..
First you need to sniff an access point e.g. by using airodump-ng, then you need to deauthenticate an aktive station to capture a handshake which is common with WPA, then you need to crack the captured ARP package with either aircrack, cowpatty or some other kind of password crack method, all depending on the dictonary list, wpa table or wordlist that you have.
So to summen up, with my knowledge so far, no there is no easy way to get a wpa key if it is not allready listed in the list provided for cracking the captured packets.
I would love to be proven wrong here