When you visit a website, you are redirected to the hosting company where the DNS is pointed for that particular site. When migrating your site to DreamHost, you can upload all content to your DreamHost server, but you will still see the old site at the old host when visiting the URL.
To see the website you've uploaded to DreamHost servers (before changing your DNS), you have two options.
Which option should I choose?
View your site using a 'hosts' file
This option is the most accurate way to view your site as it appears on DreamHost's servers, however it's more complicated as it involves editing a configuration file on your home computer. If you are uncomfortable with updating configuration files on your computer, use the dreamhosters.com option instead.
View your site using a free dreamhosters.com subdomain
This free subdomain allows you to see what the site will look like at DreamHost before you make the final DNS change at your old hosting company. This is the easier of the two options as it does not involve editing any configuration files. You can create and manage the sites within your DreamHost panel.