VAT is a hugely complex area covering a variety of different approaches depending on whether goods or services are being sold and where it was sold from and to whom. There is not enough space on this help page to go through everything relating to VAT.
A common query many business have is when they should charge VAT to non UK customers. Please note, these are "rule of thumb" guides.
Where is your customer based?
As a general top level guide, if the customer is based within the UK then you should automatically charge VAT at the appropriate rate. The VAT rate would be the same whether the customer was a business or consumer.
If the customer was EU based then it would depend on whether the customer was a business (with a VAT number) or a consumer. It would also depend on whether the sale related to goods or services.
However, if the customer is based outside the EU then generally there is no VAT charged to a business or consumer.
Business or Consumer
Generally, if the sale relates to a customer within the EU (but outside the UK) you must first verify whether the customer is a business or consumer.
Business: if the customer is a business then you need to determine whether they are VAT registered and hold a valid VAT number. Assuming they do, you do not need to charge VAT to that customer. However, if the business is not VAT registered or cannot provide a valid VAT number you must charge VAT at the appropriate rate.
Consumer: usually you would charge VAT to any consumer resident within the EU.
For more detailed guidance on how VAT is charged, especially in the EU visit the gov.uk site