To add our new User to our Group, the add() method is used as shown below.

PS > $Connection = "LDAP://Server1/CN=NewGroup,OU=NewOU,DC=APA,DC=CORP"
PS > $Group = [adsi] $Connection
PS > $User = "LDAP://Server1/CN=jeapic,OU=NewOU,DC=APA,DC=CORP"
PS > $Group.Add($User)

If we look at the memebers of the group, our user will be added.

PS > $Group.member

CN=jeapic,OU=NewOU,DC=APA,DC=CORP

In the AD MMC Snapin, we can view the changes that we made.

And if we want to remove a user from a Group we can use the Delete() method.

PS > $Group.Remove($User)

Below is the code used in this post

$Connection = "LDAP://Server1/CN=NewGroup,OU=NewOU,DC=APA,DC=CORP"
$Group = [adsi] $Connection

$User = "LDAP://Server1/CN=jeapic,OU=NewOU,DC=APA,DC=CORP"

$Group.Add($User)