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I expect my question to sound very naive, please excuse for this. I have a set of $(x, y)$ points on a graph, which are the measurements of a real-life process. Now I want to draw an "approximation line" (or "best-fit line", I don't know what is the right name for it), which should visually show a common tendency of all these measurements. Which technique/method should I use?

ps. I found a way how to do it manually, but I need an algorithm, in order to render such a line automatically.

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Start with linear regression, go from there. –  Simon Hayward Nov 26 '12 at 21:10
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If you need something simple and you would be happy getting a linear model, consider a linear regression or other similar parametric models. Otherwise, there are many methods, kernel smoothing would be an interesting one (particularly, a local linear regression is one of my favorites).

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