I am not sure if you asking how the sign-up process works, or how DreamHost hosting works in general.
If you are asking about the sign-up process, it is pretty straight forward. Once you have completed the payment process your account will be subject to approval. The time required for approval does vary quite a bit. Some accounts are approved almost immediately, while others can take some time.
If your application triggers the DreamHost fraud detection system (for whatever reason) you may be asked to submit a fax consisting of a rubbed copy of your credit-card. This is a fairly painless procedure and is DreamHost's way of determining if you actually have possession of the credit-card you are using for the purchase.
Once your account has been approved you will receive an email giving you details of how to log-in and upload your site. If you chose to register the 'free' domain during the sign-up process you will also receive an email once the domain registration has gone through.
Save [color=#CC0000]$50[/color] on DreamHost hosting using promo code [color=#CC0000]SAVEMONEY[/color] ( Click for promo code details )