As of February 2016, about 2,000 extrasolar planets have been discovered, in nearly 500 different planetery systems. You can get an up to date list of the planets discovered at this website. The properties that we know about discovered extrasolar planets are highly dependent on the detection technique used to discover them.
The technique that has discovered the most extrasolar planets, the transit method, involves looking at dips in the observed brightness of stars caused by a planet passing in front of them and blocking the light. The amount in which the brightness drops can tell us how much of the star is being blocked, which lets us know the size of the planet. Since the planet will only block its star once every orbit, by looking at how often this happens we can also determine the planet's orbital period.
Another detection method that has found many exoplanets is the radial velocity method. When a planet orbits a star, it also exerts a slight gravitational tug on the star, causing it to wobble. This method involves looking for wobbling stars that indicate orbiting planets. By looking at how much the star wobbles, it's possible to tell how massive the planet is; the more massive the planet, the larger the wobble that it causes. By measuring how the strength in the wobbles changes over time, it is also possible to determine the orbital period of the planet.
The method that can potentially tell us the most properties about an exoplanet is direct imaging. This is the only direct method of exoplanet detection, since all of the other methods involve looking at just properties of the star to infer if it hosts planets. By directly imaging a star system and subtracting out the light from the star, it is possible to then see the much fainter planets orbiting. By analyzing the light reflecting off the atmosphere of the planet, it is possible to determine planetary temperature, mass, and even composition. The main problem with this method is that it is still very difficult to achieve with our current technology. However, as more and more technological advancements are made, it is becoming much easier to find and characterize planets this way.
This page updated on February 10, 2016 by Thea Kozakis.