With MF's (or ETF's may be good for you), you are diversifying away the single-company risk you have with individual stocks. So instead of selecting good companies, you need to select good portions of the market in which to invest and then find the MF/ETF that best invests in that segment for you. Possibilities are large companies, small companies, fast growing companies, dividend paying companies, foreign companies, energy companies, real estate, and bonds, among many others. Most here would say don't try to select winning market segments, but just invest in them fairly widely so that you always have something in the next top performing segment.
So the first thing to do is decide how you want to spread your money within the possible market segments. Then select MF's that select companies mostly within that segment. That way you don't end up with five MF's that are good but all invest in something close to the S&P 500.
In addition to long-term performance, look for low costs, stable management (is the current manager/team responsible for those long-term gains?), no load, fees, tax efficiency (if applicable), and availability at your broker (or direct with the fund company).
You can't go too wrong with very low cost index funds or ETF's. ETF's at your broker that are commission free may be your best bet. For actively managed MF's look for good long-term performance (10+ years preferably) with a fund management firm that has several good performing MF's and hopefully a good management rating from Morningstar.com.
Here's the strategy I roughly follow (a "slice and dice" style that can utilize a lot of different funds):