According to the periodic table which element most readily accepts electrons?

Fluorine is the element which readily accepts electron.

Explanation:
                   Fluorine belongs to Group VII elements also called as Halogens. The electronic configuration of Fluorine (Atomic Number = 9) is as follow,

                                              1s², 2s², 2p⁵

While Electronic Configuration of Neon (Atomic Number 10) is,

                                              1s², 2s², 2p⁶
Now,
In order to attain Noble Gas Configuration, Fluorine atom tends to accept one electron readily so that it can attain Noble Gas Configuration, which is a stable state.