Good morning Forza,
The effective time frame we have noticed varies in the different Member States between two weeks and up to three months to obtain the VAT ID#.
Documents to provide are generally:
- the local forms to be filled (using the or one of the official languages

)
- an original VAT certificate to be requested from your tax authorities
- a certificate of registration of your company
Some Member States also require the deed of incorporation of your company, the full coordinates of your Tax office and any document showing that you are at the verge of starting your taxable operations (contracts, bids, tenders, quotes, proformas...). etc...
Last but not least, certified translations into local language of all documents may be required.
As a whole, weeks or months may be required between your file dress up and the effective communication of your VAT ID#. Since 01/01/2002, any EU established company may directly contact the tax authorities of other Member States for VAT identification purposes.

In practice, it is strongly recommended to use a local professional, taking into account that once the VAT ID# obtained, a steady expertise in VAT return and Intrastat is require to guarantee your company's compliance with local VAT rules.
Good luck anyway Forza!