When you first navigate to 1and1.com you will see a screen similar to the following:

Already A 1&1 Customer?

If you are already a 1and1 customer, you simply need to click on the 'Customer Login' in the top right corner. (Red arrow in the picture) This will take you to the login screen:

Here you just need to enter your customer ID number and password to get into your account.

Not A 1&1 Customer Yet?

If you are NOT already a customer, don't worry, it's pretty easy to get signed up and get your domain name. Instead of clicking 'Customer Login', you will instead click the 'Domains' option on the left, just under the phone number.

You will get a screen like:

You will be able to see any specials going on and you can enter your desired domain name in the box. (See the red arrow). Be sure to check your preferred TLD choices to the right before you click the 'Check' button. If your desired domain is already taken, 1and1 will return options including alternate TLDs or even different spelling or punctuation of the domain you entered.