These new worlds were discovered not by viewing them through a telescope but by their affect on their parent star. This page serves to explain the doppler detection method as clearly and concisely possible. If we tried to observe these planets directly astronomers would need a telescope with a mirror at least 100 meters across. This apparent difficulty and monumental engineering feat was circumvented through elementary physics.
Every object pulls on every other object gravitationally equally and in the opposite direction.
By measuring this perturbation over several years, it was calcualted as to how big and how far away a planet would have to be to generate such a wobble. The below animated GIF illustrates the planet's orbital affect on the position of its parent star. This perturbation can be measured by measuring its parent star's spectrum. The light from a star can be broken down into its constituent colors and analyzed. This 'broken down' light or spectrum contains dark and light lines which are specific to the elements, ions and molecules which make up the star.