I'm pretty much a pure mechanical investor and been doing it for about 10 years now. I use the approach you're talking about. Develop a plan, backtest it, then work the plan.
You seem to be asking "what does it mean to backtest?"
In it's ideal form backtesting is developing a set of rules, then applying those rules starting at some day in the past -just like one would have actually traded. Then see how well you do. The idea is that past performance will be an indicator of future performance.
Now, if your rules are sufficiently simple, and doesn't trade a lot (like the Dogs of the DOW strategy) you may be able to backtest by hand. Looking up historical data and plugging the numbers into a spreadsheet can work. I did that for many years downloading data from Yahoo.
There are a number of sources for price and volume (technicals) like Yahoo or MSN, but historical fundamentals like sales or earnigs are less easy to come by. Historical earnings estimates (needed for valuation calcs) are even harder.
So, if your rules are more complex or if you use any fundamental data in your strategy then you will need to use some backtesting software. There are a couple of online tools I'm familiar with. I like Stockworm.com. It has both technical and fundamental data going back over 10 years. Another site to look at would be stockfetcher.com. They only have technical data though.
Now remember, I said "in it's ideal form". Backtesting like this will give you the exact buys and sells you would have made each day over the entire span of your test. A less rigorous approach would be to simply do two-point backtesting. Apply a set of rules to "buy" some stocks at some point in the past then see what those stocks are worth now. There is also an approach that (typically technical trading software uses) where the rules are applied to just one stock. Then see when that stock would have gotten bought or sold.
In any case, backtesting is simply applying the rules you plan on using to trade with to historical data then analyzing the results.
Good luck!