What is the code to restore SQL Server databases in VB?

It's hard to tell exactly what the problem is without seeing your code. Executing RESTORE from VB.Net is not much different than executing from SQL Server. You need to construct a SQL Server statement and execute it with ADO.NET. Here is a sample for restoring the Northwind database:

Dim sql As String = "RESTORE DATABASE [Northwind] " & _
"FROM DISK = N'C:SQL Server DatabasesNorthwind.bak' " & _
"WITH FILE = 1," & _
"Move N'Northwind' TO N'C:SQLNorthwind.mdf'," & _
"Move N'Northwind_log' TO N'C:SQLNorthwind_1.ldf'," & _
"NOUNLOAD, STATS = 10"

Dim cn As SqlConnection = New SqlConnection("Data Source=rrehak;Initial
Catalog=master;Integrated Security=SSPI;")
cn.Open()
Dim cmd As SqlCommand = New SqlCommand(sql, cn)
cmd.ExecuteNonQuery()

Make sure the account you use in the connection string has sufficient privileges for the RESTORE command. If the database does not exist, the user needs CREATE DATABASE privileges. If the database already exists, the user has to be a member of the sysadmin or dbcreator server roles, or be the owner (dbo) of the database.