Linear regression books usually include a footnote that you might have to transform your data before you can apply regression. However, they seldom give any guidance on how to pick a transformation. Just try something until your scatterplots look linear.
John Tukey gave a nice heuristic for linearizing data in his 1977 book Exploratory Data Analysis. Tukey gives what he calls a ladder of transformations.
Try transformations in the direction of the bulge in the plot. If the plot bulges up (say your plot looks something like y=√x), then move up the ladder from the identity: try squaring or cubing the data. Or if you’re going to transform x, think of the ladder as horizontal, from x3 to –x-3. If the bulge is down and to the right, either move down the y-ladder or to the right on the x-ladder.
(If you know of a good presentation of this topic online, something with good illustrations, please let me know and I’ll link to it. I did a quick search and found several hits, but the ones I looked at lacked clear pictures.)
Related: Applied linear regression