First, I would be remiss if I didn't note that an address is a value type; it doesn't have identity, and should not be an entity. The Entity Framework supports such types via the complex types feature. Unfortunately, the Entity Framework designer has zero support for this (Edit: Fixed in VS 2010), so the only way to use the feature is to edit the EDMX manually. As it happens, Address is the type used in most of examples, see you might want to consider this.
Nevertheless, I will actually answer the question you asked.
The simple solution would be:
newCustomer.Address = new Address()
{
Street = streetTextBox.Text,
// etc.
};
However, since Address is really a value type (in other words, two customers with the exact same street address should probably point to the same Address object), you may want to try and select an existing Address object from the context before you just go and new up a new one.
newCustomer.Address = (from Addresses in context where ...).FirstOrDefault();
if (newCustomer.Address == null)
{
newCustomer.Address = new Address()
{
Street = streetTextBox.Text,
// etc.
};
}