To configure this for a one way trust, you will need to have an account in the target forest. This account should be a standard Domain User account and have rights to read all of the user objects you want to expose in SharePoint; this is the default config for Domain User accounts.
1) Set an Application Password. This must be done on each farm member and must be the same value.
2) Configure the People Picker for each domain you want to show. The domain in the one-way trust will leverage the user account created for you.
See https://thesharepointfarm.com/2014/01/powershell-for-people-picker-properties/.
Application Key, run once per farm member:
$key = ConvertTo-SecureString "Password1" -AsPlainText -Force
[Microsoft.SharePoint.SPSecurity]::SetApplicationCredentialKey($key)
Domain, performed once per domain with a username and password used for one-way trusts but left out for domains using a two-way trust.
$wa = Get-SPWebApplication http://webAppUrl
$adsearchobj = New-Object Microsoft.SharePoint.Administration.SPPeoplePickerSearchActiveDirectoryDomain
$userpassword = ConvertTo-SecureString "UserPassword1" -AsPlainText -Force #Password for the user account CONTOSO\s-useraccount
$adsearchobj.DomainName = "contoso.com"
$adsearchobj.ShortDomainName = "CONTOSO" #Optional
$adsearchobj.IsForest = $true #$true for Forest, $false for Domain
$adsearchobj.LoginName = "s-useraccount"
$adsearchobj.SetPassword($userpassword)
$wa.PeoplePickerSettings.SearchActiveDirectoryDomains.Add($adsearchobj)
$wa.Update()