Lots of ways. Tree rings, for one. Evidence of wind patterns such as dust and pollen transport, sea levels, species migration, soil deposits - there's actually quite a few factors that together paint a reasonably good picture of climate for thousands or even hundreds of millions of years before now.
However, if you want to know what the wind chill factor was in central Pangaea @ 20E 40N on January 4th, 210,537,896 BC at 9AM in the morning, you're kinda on your own. Science isn't THAT good.
Being able to put down citrus groves and vineyards as far north as the Scottish border was another