First off, educate yourself about investing. By that I mean gain a working knowledge about stocks, bonds, mutual funds, etc. Learn about the importance of diversification and asset allocation. Understand the role of 401Ks, IRAs, taxable brokerage accounts, checking accounts, insurance, etc., and the advantages of each.
Next, once you're ready to invest in the market, open an account at a well established discount broker. This might be a Roth IRA account, an individual taxable trading account or both. You'll need to have an initial deposit into what's called a core account from which you can buy stocks and funds. Start small by buying a few index funds like the S&P 500, a corporate bond fund, and maybe an global stock fund. Continue to expand your knowledge at research sites like Morningstar.
Mutual funds offer the ability for smaller investors to invest in a bucket of stocks or bonds instead of individual ones. But if you decide you want to invest in a particular stock, check to see whether they offer a Direct Investing Plans (DRIPs). Sometimes, but not always, DRIPs charge less commissions than buying stocks through brokerage houses.
Ask 100 people about investing strategies and you'll get 100 different answers. The best advice I can give is pay yourself out of each paycheck. By that I mean, put a small set amount each paycheck into your brokerage account, 401K, Roth IRA, etc. after setting aside what you need for living expenses. Regular investing takes advantage of the power of compounding.
Good luck.