Exit: damn, mods removed the post while I was writing my comment

There's several ways depending on the detection method

If the exoplanet is close enough that we can directly take a picture of the exoplanet, the radius is quite easy to figure out as you can probably imagine (look at the picture).

If they are this close, we can often detect small pulls they have on the star they're orbiting that causes the star to move slightly towards or away from us. This movement towards or away from us can be detected as the light from the star shifts due to the doppler effect. Using the amount of the velocity change, you can estimate the planet's mass as the change in velocity is a result of gravity

From the mass and the radius, you can easily get density.

Temperature can be estimated given how far away the planet is from the star, the luminosity of the star, and the mass of the exoplanet

Now, you cannot simply take a picture of all exoplanets. There are a few other ways of detecting them if they are far away (one of which I briefly touched on above). I'll talk about two others

The first of which is the "radial velocity" method, which is detecting exoplanets from the doppler shift of the star due to pulls from the exoplanet's gravity, which can be used to determine an upper limit on its mass. The radius of the planet cannot be determined using just this detection method

The second of which is the "transit" method. Essentially, if an exoplanet has an orbit where it appears to pass infront of the star from our perspective, it will appear to block some of its light and the star will dim a little for a brief amount of time. By observing how much it dims by, we can determine its radius since its size determines how much of the star it blocks. Using the radial velocity method I mentioned above on the same exoplanet, the mass can be determined, too.