Yes, megaengineering project that we won’t be able to pull off for many centuries (if ever), just curious as to how it could be accomplished.
Big engines?
First you have to file the paperwork.
Big engines, lots of them if the planet rotates, switching on and off as it rotates, and limited thrust not to cause too much tectonic mayhem.
The most practical method I’ve heard of to adjust a planet’s orbit would be to set yourself up with a mass driver and start hurling rocks towards the offending planet so that said rocks make a slingshot orbit around the planet. Eventually the rocks will transfer enough momentum to the planet to make a difference.
A place to stand and a lever long enough. 
Or a lot of mass.
A long enough lever and a fulcrum on which to place it.
I had not thought of those problems. Here’s a totally different idea, which will easily solve both of the above: Don’t do anything to the planet itself. Just get rid of the star that it’s orbiting around, and then the planet will simply go off on a tangent under its own inertia.
Potential problems: You can’t just break the star into pieces, because if its center of gravity is unchanged, then the planet will continue to orbit it, I think. OTOH, if the star has been spread out over a large area, such that a significant portion is beyond the planet’s orbit, then the center of gravity won’t be such a problem. Simplest approach would be to just transport the star elsewhere.
One of the ideas for diverting asteroids has been to paint half the asteroid white, point a large mirror at it to reflect sunlight, and then let light pressure slowly do the work for you. Probably the cheapest, although not the fastest option.
If you’re cunning enough, you can slingshot them around another body in the system to steal momentum from that - again and again, picking up at one end, dumping at the other.
Reminds me of a sign I once saw in a repair shop:
Done, and the plans are on display in the bottom of a locked filing cabinet stuck in a disused lavatory with a sign on the door saying ‘Beware of the Leopard.”
You just get a much bigger planet and bring it close and let the gravity tug your planet after it.
Note moving the bigger planet is not my department.
Ah, good, as long as they’re all in order. It’s Somebody Else’s Problem, now.
Larry Niven used this method in one of his novels set WAY in the future… you place a giant fusion ramscoop engine in the upper atmosphere of one of the gas giants, tough enough to last pretty much forever and with a level of buoyancy that it’ll float at a certain altitude. When you need thrust, turn on the fusion drive (as mentioned above, turn it off when the planet rotates far enough that you’re pushing it off-course; this also allows the huge engine (the size of a small moon or Death Star) to bob back up to the point where it floats). Rinse, repeat as needed until you’ve moved the gas giant into an orbit that has it pass by Venus (to drag it away from the sun) or Mars (to bring it in closer), then park it somewhere in a more stable orbit until you need it again.
The problem with this (other than that any sufficiently large amount of thrust is either going to punch through the crust or compress the mantle with associated tectonic stresses) is that the exhaust speed of the plume will have to exceed the escape speed of the planet at the surface, otherwise the exhaust either goes into orbit or falls back to the surface, and you get no net momentum transfer.
Stranger
Just try not to screw it up.
This seems like a fun project (planning it, not doing it!) for someone with good celestial motion software. Minimum-energy solution might be a like a combination shot in billiards: redirect smallish asteroid(s), via “slingshots,” to crash into or affect a larger asteroid and eventually direct the large asteroid into an Earth-interacting orbit.
Would it be easier to push the Moon away from the Earth than to affect the Earth directly? What happens to the Earth’s orbit after Moon escapes? (I suppose you’d have a lot of control, by choosing which direction the Moon is traveling when it finally goes parabolic. 
)
Wrap huge coils of wire around the planet in synchronous orbit, and use that as an ion engine?
Where are we moving the planet to? Just to a slightly warmer/cooler location, or are we going walkabout with it?
Anyone remember the sheewash drive?