Once you have registered for VAT in your chosen country, you will then be required to file periodic statutory declarations. In particular, a VAT return will need to be filed (usually every month or quarter), which summarises all the taxable transactions that your business made in that period.
Each VAT return can be different, and will have differing information requirements and reporting formats. In every cases, you must declare the VAT that you have charged on sales (output VAT).
It depends on the transaction types and values, but your business might have to pay the VAT surplus over to the local tax authorities.
There might be other statutory reporting obligations, in addition to periodic VAT returns. Within the European Union, each time you are involved in the movement of goods across EU Member States, you will be required to report such movements to the EU tax and customs authorities, including EC Sales Listings (ESL) (for B2B sales) and Intrastat Reports (subject to thresholds).