First - examine "prior art" or subject matter.
 Warp drive in your universe.
After you complete outline of technologies, you may find that Star Trek on screen used warp drive to disturb star surface (e.g. to destroy dominion shipyards) by causing a flare.
Ian Douglas / William Keith in "Galactic Corps" described species called Eulers, which used "trigger ships" (small capsules traveling at warp) to punch through the star, cause a shockwave which in turn resulted in star turning nova.
 As Star Trek TNG "Q" put it "simple - change the gravitational constant of the universe".
This was explored in details in Issac Asimov's "Gods Themselves..." -
Constants in Question were beautifully described by scientist Martin Reese in absolutely must-read "Just Six Numbers". Certain invention called electron pump allowed two universes to generate free energy by exploiting subtle differences in nuclear force strength. However, it turned out that these constants started drifting and equalizing between universes, causing slow, but meaningful change in star behaviour.
 There's option explored in Andromeda (TV series) as regular weapon (WMD by any means) and Stargate SG-1 (jury rigged) - "nova bombs" and shielded stargate dropped into the star. Both caused disturbing balance between radiation pressure and gravity in main sequence star. In first case, it was miniature "white hole" generated using combination of negative energy and exotic matter in second...well..just active stargate, sucking stellar mass.
 SG-1 in other episode beautifully told another concept: "poisoning the star" by introducing heavy elements into the core.
Note: once stars star to create iron, which can't be fused further without significant energy input, their fate is sealed.
Question is: how much is needed.
 Decade or so back, Scientific American published article about simulation regarding rouge white dwarf star hitting the Sun.
Note, that recent discovery of gravitational waves confirmed that black hole systems may exist - and that includes such, which will give stars or other black holes effect of gravitational "slingshot".
 Again "Galactic Corps" - quantum mechanics. In general, if you could map wave functions of elementary particles that compose the star, you could alter them - and possibly, the physical parameters of respective particles.
Even just "sniffing it out of existance".
 Introduce q-ball into the star as in movie "Sunshine". Again, use quantum mechanics to disturb fusion within the star.
 Brute force: find a small black hole. Throw huge star at it. Create accretion disk and polar jet aimed at given system :) problem is, that's overly excessive (why not smack original star) and limits damage to speed of light.
 Stars usually spin. There exist a neutron star (or magnetar) which is definitely too heavy and should collapse into black hole long time ago, but - as suggested in other answer - it is stabilized, presumably by fine balance between excess of mass and ultra-fast rotation.
If you could arrest some of the spin...
 LHC-like scenario create artificial singularity, project into the star, let it do the and eat it.