how does one buy an IPO? Are these only for institutional investors? For example Dropbox IPO'd at $21, yet I don't think I had the opportunity to purchase at this rate. I can buy on the stock exchange but not at that IPO price. Why is this?
Institutional investors typically get the lion's share of an IPO allocation.
On the retail side, generally you need an account with a broker that is part of the underwriting syndicate. Good IPOs are like a reward and brokers tend to allocate shares based on account assets. Small accounts tend to get little or nothing unless the IPO is a dog.
There another aspect of this when IPOs are plentiful. I was an IPO whore during the 90's internet craze when they were pricing wallpaper which often zoomed the minute trading began. Brokers buy (and steal) cold call lists. When you participate in a number of IPOs, your name gets distributed and many brokers will start calling you with offerings. I'd compare it to going to Vegas enough times to get on the comp lists. I subscribed to a good IPO newsletter/service that accurately ranked expected opening price performance. Those were the days...
Back to you. Find out what brokers are in the underwriting syndicate. Look for smaller firms (you're not going to get allocation from Goldman Sachs). Call and find out if they have any shares. You may have to fib about your net worth to get a fish to bite. Beware of anyone who offers you size because that means that there may be difficulty placing shares.