what are the two basic methods to raise capital of common stocks?

Answer 1

More detail would have been nice, as there are many ways to answer that question. Here are a few possible answers:

1. A public offering (e.g., IPO) or a private offering.

2. If only considering public companies: An Initial Public Offering (IPO) or a Seasoned Equity Offering (SEO). A seasoned offering is one where a company that has already gone public goes back and sells more stock.

3. If only considering initial public offerings of stocks, then there are several methods -- including Firm Committment IPOs, where the underwriter assumes the risk of bringing the new securities to market -- guaranteeing a minimum sale and a price -- and Best Efforts IPO where no such guarantee exists.