I'm brand new to options trading.

How do I know how many contracts are available to buy? For a simplified example, if a company has 1000 shares outstanding, I couldn't buy more than 100 contracts. But how would I know those numbers in advance?

There is no one to one relationship between shares and available options but the outstanding float on any stock with listed options will be quite large. The CBOE, for example, requires a minimum of seven million shares outstanding and there are also requirements for number of shareholders and trading volume.