Just enter the VAT number in the VAT Removal form when you check out.
The VAT number will be checked against the VIES database. Also make sure that you have selected the correct country and that the number is written on the correct form.
If the VAT Removal form doesn't appear, it's probably because you have selected the wrong country. For Swedish customers, remember that we are located in Sweden, and thus VAT is handled as any other purchase in a Swedish store. You deduct the VAT when you do your VAT report.