Probably the best place for you to get started is the BBC websitepages - specifically 'Real Chinese'.
This will give you a taste of the language and some good learning tips and you should get an idea of whether you want to take your learning further.
However useful the BBC course is, it can only give you a taste of the language. You need an awful lot of repetition, exposure and practice to begin to be able to express yourself in another language. Just think how many months you spent as a baby just listening to your first language before anyone had any series expectations that you would come out with a meaningful sentence. So set yourself reasonable expectations as you learn a foreign language - and try to get as much 'easy listening' practice as you can. This is where the internet and free language 'podcasts' can be really help out.
I suggest you explore some of the suggestions below and find one that suits you. Then use this as your main study 'thread', dipping in and out of the other suggestions to bulk up your exposure to the language and making use of other online tools such as personalised flashcards.
A word or warning, however. In almost all the suggestions below you are first asked to 'register', which is quick and easy. The 'core' part of the course is free - often the audio podcasts - but if you want to get hold of the 'extras', such as transcripts, extra material, grammar practice etc, you are invited to become a 'basic' or 'premium' member. You can learn a language without every signing up for these paid extras. I strongly suggest that, if you are tempted to do so, you make yourself wait until you've used the free material for a reasonable period of time to be sure that it's the best thing for you. Anyway ...
Chinese Learn Online is my favourite podcast to learn Chinese. It describes itself as a 'progressive' course because one lesson follows on from the next - it isn't designed for you to dip into anywhere - and they've done a great job at tracking what has been taught in which lesson. It is 'narrated' or hosted by a character called 'Adam' who has a likeable, professional tone (and sounds rather like Kermit the frog) without trying to become your new best friend - which makes a pleasant change from many language-learning podcasts. Adam isn't a native speaker, but is almost always accompanied by at least one other native speaker of Mandarin. The team also make sure that you are exposed to a variety of Chinese accents, which is very important.
What's more - and very unlike most language podcasts - Adam and team try to minimise the use of English in the podcasts, weaning you off dependency on instructions in English by teaching them to you in Chinese - little by little.
The teaching approach is excellent, providing the right blend of challenge, repetition and reassurance. Furthermore, if you download the free lessons and listen on an iPod (or similar) the tapescript of each dialogue is displayed on screen for free. This means you can follow the tapescript for free; (most podcasts make a charge for the tapescripts) and don't have to print out a pdf to have it handy when you're out and about.
To download the audio files from the beginning (Lesson 1) go to the tap 'Resources' and then select 'Bulk Downloads' (See image below).
Another favourite podcast site is Serge Melnyk's.
Like Adam, Serge is a non-native speaker of Chinese, but unlike Adam he would often pass for a native speaker, I expect and, as a result, handles most of the dialogues by himself, or with a little support from Chinese friends. This makes his pronunciation super-clear and very reassuring as you get started with the language. You have to pay for the transcripts though. Another more minor gripe is that Serge believes in 'pre-teaching' all the vocabulary you're going to meet in each dialogue. Now you may like this, but I find it becomes pretty mind-numbing after a while; I wish he would cut to the chase and let me try to understand what I can from the dialogue - before hearing the explanation and translation.
Another podcast site you might find useful is 'Chinesepod.com'.
Here's an example audio file that you can find there:
Although all the English which is spoken before you ever get to any Chinese, along with the relentless cheeriness of the the hosts, can be wearisome, many people find these podcasts helpful. Unlike the other two 'courses' above, each lesson deals with a shorter piece of Chinese dialogue and tends to be very functional - for living/visiting/surviving in China. The site isn't the easiest to navigate. You also to have to learn that when they talk about 'Channels' they are referring to language level: newbie (beginner/false beginner) Elementary, Intermediate etc, whereas 'Sets' refer to a group of connected/themed lessons.
Sign up for the 'free trial' if you like - but if you want to keep things free, remember that it's mainlythe audio lessons that you should get used to. (You'll see a selection from the 'Newbie' section towards the top of this page, in the left hand column). There are other resources that you can use for free - such as the grammar reference, but this is of only limited use because it is written in an almost incomprehensible style.
Livemocha is a great place to learn vocabulary and phrases. It bills itself as a 'Social Language Learning' site - but you can be as unsociable as you like and just use the resources. Get a free account, choose the language you want to learn and off you go. The main problem with Livemocha if you're learning Chinese is that it presumes that you want to learn Chinese writing. If, like many people, you are more interested in learning to listen and speak Chinese but balk at the thought of all those characters, you are limited in the resources you can use. Although in the 'Learn' and 'Review' sections of the lessons 'pinyin' is used, in the speaking and writing sections you are expected to know the characters. As a result it's difficult to 'complete' a lesson or participate fully with the activities. But hey, it's still good stuff - and provides masses of that all-important repetition.