In case someone else stumbles on this, because it's not documented anywhere, I managed to figure this out.

var mainQuery = new GroupQuery(LuceneOperator.AND);

var categoryQuery = new CategoryQuery(LuceneOperator.AND);

foreach (int categoryId in CurrentPage.Category)
{
  categoryQuery.Items.Add(categoryId.ToString());
}

mainQuery.QueryExpressions.Add(categoryQuery);

var result = SearchHandler.Instance.GetSearchResults(mainQuery, 1, 20);

Cheers
Fredrik

Thank you Fredrik!

/Erik