In the National Geographic article about NASA's announcement of new planets discovered by the Kepler spacecraft, it states that there are 4,175 candidate planets. What is the process for vetting these candidate planets? How do we know they exist without knowing whether they are planets? Or are they candidates because the data hints that a planet might be there but we need more detailed data or more analysis before we can confirm it?
Planet "candidates" are Kepler Objects of Interest (KOIs)that have a transit-like light curve and have passed a number of observational tests. They are candidates, because although they do show a transit in the light curve of the star in question, there is no independent confirmation of a planetary mass.
One problem to overcome is that of "false positives". There are other astrophysical phenomena besides planets that can mimic an exoplanetary transit in a Kepler light curve. For instance a grazing incidence stellar binary can produce what looks like a transit in a light curve; so too can a chance alignment of a star with a background eclipsing binary star. There are also a number of instrumental anomalies, such that a signal in one part of a CCD or the Kepler field can produce a "ghost" at another position that might look like a transit.
If you can obtain detailed spectroscopy including accurate radial velocity measurements you can usually rule out most of these false positives, largely by getting a mass constraint for the companion.
Even where you have a very clean transit signal and can estimate a planetary radius, a further problem is that a wide range of masses produce objects with very similar radii. ie. more massive brown dwarfs have very similar radii to exoplanets. Again, only a mass estimate, either through radial velocity measurements or sometimes through "transit timing variations" if the object is in a multiple exoplanet systems.
Now the problem with the KOIs is many of these stars are way too faint ($V>14$) to do the kind of detailed spectroscopy that is easily possible on the much brighter exoplanets around stars found in say the HATNET or WASP ground-based surveys of bright stars.
So, what you can do is tackle the problem statistically, by identifying the kinds of false-positives you might have, quantifying their influence, and throwing away suspect objects (see for instance Batalha 2012). Section 4 of this paper describes in detail some of the tests that are done: e.g. comparing the depths of odd and even numbered transits to look for asymmetries that would indicate grazing incidence binaries; looking between transits for a secondary eclipse that would also indicate a stellar companion; the shape of the transit is diagnostic but cannot easily rule out a planetary candidate; searching for motion of the "photocenter" of the source - if the photocenter moves during a transit it could indicate a background, diluted, eclipsing binary lightcurve.
An early paper by Morton & Johnson (2011) claimed on the basis of a population synthesis approach, that that astrophysical false positives were limited to less than 10%. However, a recent paper by Coughlin et al. (2014) discusses how instrumental effects can be tested for by comparing the transit periods with the periods of other known objects in the Kepler field of view. They claim that around 30% of the KOIs may in fact be false positives. Either way it looks like the big majority of the KOIs are indeed exoplanets, but identifying which ones aren't will require detailed follow-up.