You can operate as a sole trader. One owner owns a business and bears all the profit and losses. You have umlimited liability for the debts and pay only personal income tax. The business terminates by the death of the owner. 
The second option is to form a partnership. It is based on informal agreements which can be often unwritten. It is dissolved by the death of a partner. 
The next option is to set up a limited company. Liability can be limited by the quarantee or by the shares.It must be registered by the registrar of companies. The company can be established with a perpetual life. The corporation is subjet to pay corporate income tax and personal income tax.