<p>I want to use the  MultipleLookupField control in a web page that will run in the context of SharePoint. I was wondering if anyone would help me with an example, which shows step by step how to use the control two display two SPField Collections.</p>

I'm not entirely sure I understand your question, especially the bit about displaying two SPField collections. Sorry if this turns out to be the answer to a completely different question!
Anyway here's a quick demo walkthrough of using the MultipleLookupField in a web part.
Create a team site. Add a few tasks to the task list. Also put a document in the Shared Documents library. Create a new column in the Shared Documents library; call it "Related", have it be a Lookup into the Title field of the Tasks list, and allow multiple values.
Now create a web part, do all the usual boilerplate and then add this:
```
```
Label l;
MultipleLookupField mlf;

protected override void CreateChildControls()
{
    base.CreateChildControls();
    SPList list = SPContext.Current.Web.Lists["Shared Documents"];
    if (list != null && list.Items.Count > 0)
    {
        LiteralControl lit = new LiteralControl("Associate tasks to " + 
                             list.Items[0].Name);
        this.Controls.Add(lit);

        mlf = new MultipleLookupField();
        mlf.ControlMode = SPControlMode.Edit;
        mlf.FieldName = "Related";
        mlf.ItemId = list.Items[0].ID;
        mlf.ListId = list.ID;
        mlf.ID = "Related";
        this.Controls.Add(mlf);

        Button b = new Button();
        b.Text = "Change";
        b.Click += new EventHandler(bClick);
        this.Controls.Add(b);

        l = new Label();
        this.Controls.Add(l);
    }

}

void bClick(object sender, EventArgs e)
{
    l.Text = "";
    foreach (SPFieldLookupValue val in (SPFieldLookupValueCollection)mlf.Value)
    {
        l.Text += val.LookupValue.ToString() + " ";
    }
    SPListItem listitem = mlf.List.Items[0];
    listitem["Related"] = mlf.Value;
    listitem.Update();
    mlf.Value = listitem["Related"];
}

protected override void OnInit(EventArgs e)
{
    base.OnInit(e);
    EnsureChildControls();
}
```
```
Granted, this is borderline ridiculous -- everything is hard-coded, there is no error-handling at all, and it serves no useful purpose -- but it's only meant as a quick demo. Now build and deploy this web part and add an instance of it to your team site's homepage; it should allow you to get and set the tasks which are associated with the first document in the library.
The strange bit towards the end of the button Click handler, where we read a value from mlf.Value and then write it back again, appears to be required if you want the UI to stay in sync with the actual list values. Try omitting the last line of bClick to see what I mean. This has been driving me nuts for the last hour or so, and I'm hoping another commenter can come up with a better approach...