Before a public company can do a secondary offering (issue more shares) do the majority of current share holders need to approve it? or can they issue more shares without having the current shareholders vote for it?
A public company does not need a majority approval from share holders to do a secondary offering.
Note that there are two types of secondary offerings. From Investopedia, What Is a Secondary Offering?
A secondary offering is the sale of new or closely held shares by a company that has already made an initial public offering (IPO).
There are two types of secondary offerings. A non-dilutive secondary offering is a sale of securities in which one or more major stockholders in a company sell all or a large portion of their holdings. The proceeds from this sale are paid to the stockholders that sell their shares. Meanwhile, a dilutive secondary offering involves creating new shares and offering them for public sale.
A non-dilutive secondary offering does not dilute shares held by existing shareholders because no new shares are created. The issuing company might not benefit at all because the shares are offered for sale by private shareholders, such as directors or other insiders (like venture capitalists) looking to diversify their holdings. Usually, the increase in available shares allows more institutions to take non-trivial positions in the issuing company, which may benefit the trading liquidity of the issuing company's shares. This kind of secondary offering is common in the years following an IPO, after termination of the lock-up period.
A dilutive secondary offering, also known as a follow-on offering or subsequent offering, is when a company itself creates and places new shares onto the market, thus diluting existing shares. This type of secondary offering happens when a company's board of directors agrees to increase the share float for the purpose of selling more equity. When the number of outstanding shares increases, this causes dilution of per-share earnings. The resulting influx of cash is helpful in achieving the longer term goals of a company or it can be used to pay off debt or finance expansion. Some shareholders shorter-term horizons may not view the event as a positive.