There are, of course, hundreds of ways to go about this part. You'll hear about the P/E ratio (share price divided by profits per share). You'll hear about the stock chart and where it has historically bottomed and what the current plateau means. You'll hear about free cash flow and debt-to-earnings and coverage and analyst recommendations to buy/sell/hold. Most of this is really good, useful information. But none of it is the deciding factor.
You need to start reading. That's all it is, just reading. You don't need to sign up for a special advisor service or the newsletter of a particular brokerage or an recommendation service. You can, of course, but it's not necessary. Nearly all the information you need to learn details about a particular company is available online, for free.
Let's say you're interested in General Motors because your dad has owned a series of GMC trucks over the years and has never so much as glanced at a Ford, and you were pleasantly surprised with the Chevy you rented recently on a business trip to Atlanta. (As of this writing, GM is about to be criminally indicted for negligence for failing to report and misleading investigators regarding 10 years' worth of faulty ignition switches, but whatever.) Just an example.

Next, visit Yahoo Finance. For close to 15 years, Yahoo Finance has been the best starting point for public company information, bar none. Much as I depend on Google, they don't even come close on this. At Yahoo Finance you can search by company or ticker symbol (GM for General Motors, AAPL for Apple, XOM for Exxon, etc) by entering it into the Quote Lookup box. You will find a treasure trove of information. The first page you see will summarize the company from a stock investor's perspective. You can examine at customizable charts, learn about executive leadership and how much stock they own, revenues, earnings, debt, total market cap (how big is the company in dollars?), and on and on. This site is an investor's data paradise.

Where to begin? Start by perusing the list of article headlines regarding the stock you're interested in. Some will discuss the company's financial positions, some will look at a legal development. There will be pieces on the company brand, product changes, leadership changes, competition, new markets. Just dig in. I will get specific on what to look for in a future post, but for now, your job is just to get to know the company: its leaders, its plans and its track record, the markets it does business in, the companies it competes with.
Ugh, sounds like a lot of work. Of course it would be so much easier to just plunk your money down on a recommendation from a knowledgable broker referred by a friend, or from your boss who's been "playing the market" for years and who dresses better than you. But you're thinking about buying into a business. You're going to be betting money that the company you choose will be more valuable tomorrow than it is today.

Drifting to Fifty | Random unrelated nugget of the week
Pay it forward: once in a while, buy the cup of coffee for the woman behind you in line, or the next guy's hamburger, or movie ticket. You'll feel great, and you just might start an epidemic.