Which one of the following can the transit method tell us about a planet?
-its mass
-its size
-the eccentricity of its orbit

The transit method allows detecting distant planets by measuring the attenuation of the brightness of a star when a planet passes between it and the Earth.

This is done based on a phenomenon in which a body (a planet in this case) passes in front of a larger one (the star), blocking (eclipsing) its vision to some extent.  

So, this transit reflects the ratio of the size of the star and size of the planet. Hence, the larger the planet, more noticeable the eclipsing effect.

This is how the size of the star can be determined through its spectrum photometrically, although it does not give information about its mass.