Whether investing overseas or domestically, I always recommend focusing on the things in your control because you can't control what the market will do. Therefore, I encourage you to focus on keeping your costs low and your diversification as broad as possible.
To achieve this when investing in overseas markets, I use Vanguard's FTSE All-World ex-US ETF (symbol: VEU). It has an expense ratio of 0.22% and holds 2,332 unique companies as of December 31, 2011. It invests primarily in more mature, developed non-US countries, but it also has emerging market exposure.
This is the fund I use in my personal portfolio and recommend to my clients. But I never recommend this fund or type of investment in isolation. I would only invest in a broadly diversified portfolio that held this fund along with a low cost, broadly diversified domestic equity fund and a high quality, low cost fixed income fund.
For more information on the Vanguard FTSE All-World ex-US ETF: http://goo.gl/e8h8O
Nancy, This is nicely summarized and scratches the surface -
First and foremost, you need to be diversified across the globe. Do not make any big bets on any one particular country. You will need a mixture of developed and emerging markets. Although the latter category has greater growth potential it has a great deal of risk and volatility. Next keep you investment expenses through the use of Index and excahnge traded funds. Finally, consider a Value and Small Cap Value tilt, per French and Fama, to your international investments.
I agree with Russ, that VEU would be a nice piece of your portfolio. Another option is to find an advisor who uses Dimensional Funds (you can not access them directly) they have been doing International value well for many years