Hi,
You have to decide whether you want to go with a free hosted blog service or a self hosted blog...
1. free hosted blog services, like BlogSpot, WordPress.COM and Yahoo360, are free to use, but you do not own the blog and you are limited with what you can do with them.
2. Using a "self hosted" blog, such as WordPress.ORG, means that you will need to pay for a domain name (~$8) and hosting ($8+), but you then own your own domain and blog and you can choose exactly what you want to do with it, it can't be closed down by someone else, which can and does happen sometimes with fre hosted blog services.
starting with a free blog service seems the obvious choice, but remember you won't be able to transfer all of your content and the links to your blog to a new self hosted blog at a later date.
If you are just interested in blogging for fun and to try it out then go with the free option, but if you discover you do enjoy it and want to build it in to a "business", then I would recommend moving to a self hosted blog asap.
All of the worlds top bloggers, like Darren Rowse (problogger.net) and Chris Garrett (ChrisG.com), have self hosted blogs, as it gives them total control over their own blog business.
It is possible to make aliving as a blogger, but it won't happen over night, it does take persistance and a willingness to learn and stick at it.
To start you need to decide on what you would like to blog about, preferably something you already have some knowledge about, but make sure you pick a topic that is fairly popular so that there will be lots of other people who are interested in it.
To get people to start visiting your new blog you not only need to post to it regularly, you should also take part in BlogCarnivals and visit other popular blogs in the same "market" and leave good quality comments in reply to other peoples posts.
You can also use social bookmarking sites (such as Digg, StumbleUpon and Del.icio.us) to get more interest in your posts and new visitors.
Once you start getting visitors to your blog you can then start to "monetize" your blog in a variety of ways: -
1. Google AdSense - where you place a bit of code on your blog, which then displays adverts that are relevant to your content, and if a visitor to your site clicks on the advert you will get a share of the revenue from Google, the actual amount varies a great deal according to the "topic", for example "mortgage" related ads will earn more than adverts about Tattoos, but the flip side is it's easier to get traffic for Tattoos than for mortgages.
2. Selling Adverts - As mentioned in a previous answer, this is only really viable as your blog becomes more popular and recieves more visitors, but when that happens it can be a failry significant income.
3. Selling Links - This is discouraged by Google, but once your blog has PageRank of 3 or higher you can start selling text links on your blog and it can be a good, recurring, "hands free" income.
4. Affiliate Marketing - This is the simplest way to start. You can find products where the owner will pay you a commission whenever you send them someone who buys their product, often as high as 50% with information products (ebooks) from sites like Clickbank.com.
All you need to do is write a review of the product with a recommendation and include your affiliate link.
Obviously you should choose products that are related to the topic of your blog, for instance if you write a blog about dogs then you can recommend products that are of interest to dog owners.
5. List Building/Running a Newsletter - For long term profits the best method by far is to start a newsletter. You can encourage people to sign up for your newsletter by offering a free report (e.g. top 10 puppy training tips), and once people subscribe to your newsletter you can send them offers for more affiliate products each week.
You can find some free videos on how to set up a blog here:
http://blogtactics.com/videos/
hope this helps,
Matt Garrett