There are two types of shares which the companies issue including common shares and preferred shares. Companies can also issue warrants which is also considered equity. There are different methods which the company selects for issuing shares. Its a complete legal and lengthy process and I have given the link on which the step by step complete process and requirements are given. The company gets the authorized shares after being listed on the stock exchange or over the counter market but company issues less issues than the authorized shares. Please click on the link for complete method:
Issuing shares
Issuing shares