How Can you Join?
To join Adsense you will need an already operative website. If you've got that check out the programme policies to make sure that your site is in compliance with the terms.
Once you're happy with your site follow this link, click on the "Click Here to Apply" button, fill in your details and wait for your approval email. You will normally receive this between 24 and 72 hours after your application.
What If My Application Is Rejected?
Sites do get rejected by Google but this is not necessarily the end of your experiment with Adsense.
If you've read the polcies and are sure that your site doesn't breach any of the terms send Google an email asking them why you have not been accepted into the program. They will normally respond.
If you think that your site fails one of the pre-requisites then once you've made the necessary modifications either resubmit your application or respond to your rejection email with details of the modifications you've made.
Alternativelly, if you have more than one website submit a new application using one of your other websites in the application form.