Cubic Spline Interpolation...Wtf I don't understand

I have a data:

0.5--0.000346

1.0--0.046467

1.5--0.219274

2.0--0.358386

2.5--0.418706

3.0--0.439846

3.5--0.44676

4.0--0.448971

They ask do cubic spline to interpolate the inflection point. I don't understand anything. Whoever invented cubic spline was a math nerd or something, I'm an engineer and I don't understand.

I'll tell you what I do understand. I understand that I need N-1 cubic equations, 1 in between each point, and for each equation I need to find a,b,c and d. I already used a cubic approximation around the inflection point successfully but that's only one equation for all the points...cubic spline is several equations, 1 in between each point so it's not cubic spline.

Can someone show me how this works or give me a link to a __NUMERICAL__, __STEP BY STEP__ example?

Thanks guys!