Take ships intact when possible
Acquire a Crew Teleporter so that you can send boarding parties over to capture ships intact. Intact ships tend to yield more scrap, plus sometimes other benefits such as free crew members (such as when you take over a slave ship). Starving them of O2 is also a possibility, but I personally have trouble making that one work very often.
Don't be afraid to accept surrender from enemies that are near death, particularly in early systems. Not only are the rewards often as good or better than what you'd get if you destroy them, but it means the fight ends sooner and you end up taking less hull damage compared to finishing the fight out (assuming you didn't completely outclass them). Later in the game this seems to change a bit and destroying them is often worth more than having them surrender (unless, again, they'll beat up your hull a lot while you finish them off).
Scrap Recovery Arm
This one is pretty obvious. Get the Scrap Recovery Arm in the early sectors. The earlier you get it the earlier that +10% scrap bonus will pay back the 50 credits you had to spend on it. Probably not worth picking up in, say, Sector 7.
Make use of the "special" traders
You'll often run into special encounters where you can trade fuel for missiles, drone parts for scrap, etc. Decide early on what your end-game strategy is and sell the stuff you don't need whenever possible. If you're not going to use drones, unload those drone parts every chance you get, since you won't have any other use for them. Keep an eye out for good deals. Even if you plan on using missiles, trading 2 missiles for 10 fuel is a good deal unless you've already got a huge surplus of fuel. Also, and this can be risky, don't always repair your hull to full at a store in the early sectors. You can probably get by on half hull unless you get really unlucky, and there are quite a few encounters that let you repair hull cheaply or even for free. I tend to start repairing to full at stores starting around sector 6, because by then I've got enough time invested in the game to not want to die to bad luck. Early on, though, it's worth the gamble to me.
Know when to hold 'em, know when to fold 'em
In the early sectors, you want to hit every node possible before the Rebel fleet catches up with you. The more scrap you get now, the higher you'll stay on the power curve, which means you'll be better prepared for later encounters. This in turn means you'll have less hull repairs and be in a better position to take tough enemy ships intact. Personally, I'd rather risk it all and die spectacularly in the first three zones then play them super cautiously and load all that risk into the later zones that I'm now ill-prepared for. If I'm going to die, I want it to happen early!
That said, though, know when sticking around in a fight isn't worth it. Assuming you maximized your encounters in the first few sectors, by the mid point you might want to start avoiding tough encounters and just warp away. Ships with high shields and strong missiles often aren't worth the cost of fighting, since by the time you destroy them you've taken a ton of hull damage. This effect is amplified in zones with asteroid fields, ion storms, or solar flares. Speaking of which...
Consider getting Long-range Scanners
I wouldn't get these until about sector 4 or 5, as I tend to have better things to do with my scrap before then, but these are pretty cheap and can be a huge benefit in saving your hull from a trashing. I find that early in the game, I can weather ion storms fairly well, but later in the game losing 50% of my power severely hampers my ability to compete with enemy ships, which don't seem to have lost 50% of their effectiveness. This can often be a quick ticket to game over for me if I run into a tough enemy ship, as it can rip me apart pretty quickly.