I think the article explains it all better than I ever could:
…John Elliott of Leeds Metropolitan University believes he has come up with software which at least will decipher the structure of their language – and be the first step in understanding what they are saying.
Dr Elliott’s programme would compare an alien language to a database of 60 different languages in the world to search see if it has a similar structure.
It would work great at deciphering our own human languages to start with! Imagine having a universal translator pinned to your lapel!
Because languages have different word orders, Dr Elliott is amassing a library of the syntaxes of 60 human tongues.
If a message is received from outer space, it could be compared against this database. Scientists would then be able to see if it resembled anything human, or a mix of Earthly languages.
The tiny kink in the plan, of course, is that we receive a written alien language before a spoken one…
Mind you, Dr Elliott might just have the perfect people to contact to test his program. According to sci-fi site io9.com, there are people who specialize in building non-human languages:
they’re called conlangers, and they construct elaborate languages for fun or to make the portrait of an alien race more believable.
Conlangers include everyone from Marc Okrand, the linguist who wrote Klingon, to the nerds who invented the most perfectly logical language in the world, known as Lojban. Anthony Burgess invented a little conlang for his characters in Clockwork Orange, and Suzette Haden Elgin’s Native Tongue trilogy is all about a group of rebel women linguists who create their own language to subvert their ultra-sexist society. Sometimes Hollywood employs conlangers to make alien talk seem more realistic[...]
Now that sounds like a really fun job!