To get started with AdSense, you of course need an AdSense account. Visit Google AdSense to sign up for your account. Click the "Sign up Now" button on the upper right hand corner of the screen. Fill in all the information required on the screen, which includes: the URL of your website, the language of your website, your account type (business or individual), and all the payee information, which must match your bank account. Be sure to include your full name, email address, physical address, and telephone numbers. Before you submit the information, you'll need to make sure you check all the boxes to assert that you agree to all the policies. This is standard, and basically lets Google know that you will not be clicking your own ads to generate income, that you have read all the policies, and that you do not already have an approved Google AdSense account. This is important, because you can use the same AdSense account across multiple websites, so you will save time in the future.
You should receive notification within a few business days that your account has been approved. When you recieve this notification, you'll be able to login to your account. Before you can do anything else, you'll have to agree to terms and conditions, and then you will see a page that will display your current earnings, along with which ads are making you the most money.
The setup section is where you will go to generate the code that you will need to paste in your website code in order to start displaying ads on your website. You'll have several options here, ranging from textual ads, photo ads, video ads, etc. You'll be able to configure the ads to your desired space and layout, along with a desired color scheme so that the ads match your website. After you design the ad, you'll be given a javascript code to copy and paste directly in your page code.
The account section is where you will go to update contact and tax information. Google AdSense must have current contact information, and updated tax information on file at all times, so as to keep your account in good standing. You will receive a tax document that will show your earnings for the year.
Now you'll be able to get your Google AdSense account up and running with ease. Stay tuned for more on Google AdSense, including information on creating your first AdSense ad, and monetizing your website with AdSense!