If I wanted to write a second Sql query for another object on the form, would I be creating a new adapter with sql code and adding it to the same dataset?
yes u can use the same dataset and adapter.
Declarations
Code:
 Dim conn As New SqlConnection("Server=CHEETAH;Database=NorthWind;Trusted_Connection=True;")

    Dim adapter As SqlDataAdapter
    Dim ds As New DataSet()
used it to fill Categories table to dataset
Code:
    Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        adapter = New SqlDataAdapter("select * FROM Categories", conn)

        ds = New DataSet()

        conn.Open()
        adapter.Fill(ds, "Categories")
        conn.Close()

        Me.DataGridView1.DataSource = ds.Tables("Categories")
    End Sub
used it to fill Employees table to dataset
Code:
    Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click
        adapter = New SqlDataAdapter("select * FROM Employees", conn)

        ds = New DataSet()

        conn.Open()
        adapter.Fill(ds, "Employees")
        conn.Close()

        Me.DataGridView1.DataSource = ds.Tables("Employees")

    End Sub
When u use to fill data to dataset filled before, previous data clears and adapter fill new data in the dataset.
u can also clear the dataset using the clear method of dataset.