We don't. Some attempts have been made to calculate a radius or infer it from experiments. But this question is a great mystery to modern science.
To be perfectly honest, the best experiments have only put an upper limit on the radius of an electron. But, so far, they still seem to be infinitesimally small points. They are not made up of anything else.
You might expect that if you were to bounce electrons around hard enough that you might see them crashing into one another in a way which would suggest their size. If you think of them like balls on a pool table, you might expect a few to bounce differently depending on how they collide. But these experiments have not shown a hard radius.
You might ask: "How small could they possibly be?" We have reason to believe that the smallest distance scale in the universe is something we call the Planck Length. This gives you a size of about
Here's a great discussion about some of the things we know and the attempts to measure the size of the electron: How Big Is The Electron. Some of this information may be readable for the general public. But most of this article seems to be targeted at a someone who has taken several classes in college physics.