When you have a SharePoint farm and you want to use accounts from another domain you need a partial (one-way) or a full (two-way) trust between those domain. A full trust is not always desirable and there your problem begins. After setting up the one-way trust you can authenticate with an account from the trusted domain, but the SharePoint People Picker doesn't show any accounts from this domain. It has been documented by others before, but as I ran into this recently I'll give my summary how I fixed this.