There are a lot of approaches. The Spitzer results in the OP here, and the JWST concept above, is about characterizing exoplanet atmospheres during a transit using spectroscopy.

The concept you link is a "starshade". It's a sister concept to a "coronagraph" -- both use an occulting disk to block out the light from the host star, so that a non-transiting exoplanet can be observed.

One goal is to image exoplanets directly, and another is to gather spectra for characterization. One of two current mission studies doing studies of the two approaches is HabEx (http://www.jpl.nasa.gov/habex/). Obviously, the starshade is more complex/cumbersome/expensive.

Using one method or another, you have to achieve a contrast of about 1e10 between the star and the exoplanet. For every 1e10 photons that come in from the host star, your starshade/coronagraph has to let at most one get through to the detector.

It will depend on the size of the telescope, but for all practical purposes, these planets are too close to their star to see directly. A starshade will be good for Earth-like planets at Earth-like separations around Sun-like stars though.