There is a package called BBC Greek Language and people which is quite good and is the basis for two years ( 6x12 week terms of one x 2 hr lesson per week ) evening classes .
You get a book which gives all the basics plus audio tapes or discs to work to .
The book is a little bit dated now , but if you ignore the mentions of Drachmae and the prices being a quarter-century old , all else is stuff that does not age .
And you CAN get a lot of basic vocabulary , useful phrases and some grammar from that working on your own , although you really need a native Greek speaker to work with .
As well as things like Rosetta Stone , there are some Greek Language lessons on You-Tube , but a huge amount of Greek films , TV programmes , Documentaries and music and song on there as well , so you can be listening to Greek on a daily basis ( and listening and comprehending key words is the secret )
Learning a new language by a native speaker is so much easier. See if there's a Greek community where you live and ask around to see if there's an Greek teacher in the area who could teach you the language. You could always use the internet as well to learn Greek. Just google Learn Greek and see what you can come up with.
I started by learning longer sentences i would actually use - for example .. instead of just the PLEASE and THANKS etc I would think of what i wanted to say - .. "hello I am Bill this is my wife, how are you?" knowing I would have to say that the next day. this increased my Greek enormously. I now speak Greek reasonably well but not hyper fast.
On Facebok there is this group mostly of Britons who are doing just what you want. Try f/b "Learning Greek" or "Show me Basic Modern Greek".
I am sure you will find it very helpful and friendly.
I have three Rosetta Stone language programs which I find quite useful. Once the program is installed on your laptop, it goes where you go.
You can start here:
http://www.bbc.co.uk/languages/greek/
http://www.xanthi.ilsp.gr/filog/
