If you're a sole trader or freelancer, it's very similar to opening a personal account. You'll need some photo ID (driving licence or passport) and proof of address (usually a utility bill or mortgage statement).
If you're a limited company, you'll need the above, plus details of your company's registration at Companies House. You'll also likely need your tax and VAT registration details.
If you're unsure, check with your chosen business account provider as to what documents and information it requires to open your account.