You add sub-domains exactly the same way as full domains, in the panel at Domains -> Manage Domains -> Add New Domain / Sub-Domain, just enter the full sub-domain in the Domain to host: box before hitting the Fully host this domain now! button.
Actually, if you want to provide hosting for others under your account, sub-domains are probably the easiest way to arrange things. Simple create a new machine user for each person, then create a new sub-domain under the control of that particular user. This way, when they FTP to their sub-domain, they will only see the files relating to their sub-domain.
Edit: Your screen capture indicates that you are not inputting the full sub-domain. You need to enter something like always.mydomain.com
Save [color=#CC0000]$50[/color] on DreamHost hosting using promo code [color=#CC0000]SAVEMONEY[/color] ( Click for promo code details )