In order for your product to be certified/labelled organic, you need to respect a certain amount of requirements.
For example, for a product to be considered organic, 95% of the ingredients must come from organic plants or animals, and no artificial colourings and sweeteners can be used. There are some exceptions though for ingredients that are not organically available. You also need to avoid artificial fertilisers and pesticides, use crop rotation, and control weeds, pesticides and diseases.
Your product will then need to be approved by an organic certification body. A good source of information is the Soil Association, a certification body. It usually takes a couple years to be able to be considered as organic. Once you do get the certification by complying with strict requirements, inspections will be conducted every year to make sure you still comply with the rules. You will be issued with a certificate along with a trading schedule. The certificate will be like a passport to your products that proves that it is indeed organic.
When you consider exporting your organic products, the certificate will be required along with a Certificate of Import, which states that the product is produced to organic standards equivalent to the EU standards.