No one really knows what an actual space battle would look like, or even how it would be conducted. The conditions we're used to on Earth — having an atmosphere and the pull of gravity — aren't so applicable in the vast expanse above us. Of course, we can still theorise about the details based on our current knowledge and well, if you were expecting Star Trek or Star Wars to be on the money, prepare to be disappointed.
As Joe Hanson explains in this video from PBS' online series "It's Okay To Be Smart", fighters wouldn't have to constantly fire their afterburners to maintain speed, thanks to Newton's first law of motion. Explosive weapons would be "kind of useless", instead, we'd just be shooting nukes at each other and hoping the radiation melts hulls (and the people inside of them).
How about lasers? The distances they'd have to travel would render them less-than-effective, with the beam dispersing over too wide an area to deal significant damage. In fact, your best bet would be kinetic weapons — launching objects as fast as possible, with Hanson saying something like the Death Star would have been better off tossing asteroids at planets, rather than a massive ray of energy.
Not that any of this would matter. The speed of light would make targeting enemies — and even communicating with friendlies — difficult.