This is my first day using Drupal, and I apologize in advance for such a basic question. I am using Drupal 7.26 with no modules installed and when I try to sign up new users the e-mail notification is not being sent. I tried signing up with two different e-mail addresses and checked the spam folder in each account. I also tried to find an answer on the internet but I'm not having much luck. Can anyone provide some suggestions on how I might troubleshoot this issue? I've been to my Administration>Account Settings and Administration>Site Information but I'm not seeing anything that looks obviously amiss.
Install and use the SMTP module: https://drupal.org/project/smtp - Period. Nothing comes close to using SMTP and you'll avoid current and future headaches. Details are below. Good luck!
Why sending via the server is bad:
The post recommended by Anil Sagar is good. However, based on my expertise with web hosts, especially DreamHost, you want to avoid at all costs sending emails from your server.
By default, Drupal sends email via the server it's residing on. That server might not have email configured. That server might have email configured now, not properly configured in the future. That server might get spam listed in the future. In summary, a lot of things might happen that leave you without email sending capabilities, and most probably you will not be notified of the issue.
Also, you're lucky that your email is "not working" as, in most cases, some emails via the server will be sent, others will not, which is even worse as you'll not even know you have a problem to fix.
Why sending via SMTP rocks:
When you send via SMTP, you're relying on an external dedicated mail server. Choose a solid mail server provider (Gmail, Yahoo, Zoho, etc) and you'll be on the safe side. They handle maintenance and everything for you and all you have to worry about is the first step which is setting up and installing the SMTP module.
Note about SMTP sending limits:
If you're sending a large number of emails, most good email providers will have a daily limit that you'll reach and they'll stop sending your emails. This is a way for them to fight spam. For Gmail, I think the daily limit is 250 emails, which is plenty for most needs. If you have larger volumes, you might want to buy a paid SMTP account with a large limit or consider something like: http://www.mandrill.com/ - You can send up to 12,000 per month for free. They also have a Drupal integration module: https://drupal.org/project/mandrill
And if you're sending a large number of emails via your own server, you're ending up on a spam list from day one and your emails will soon not even reach junk mail.