Surtling cores are the glowing red-orange cubes that power your whole early game. No cores means no 
Smelter, no 
Charcoal kiln and no portals, so a decent stack early changes everything.
Source one: burial chambers, the skeleton caves
Burial chambers are the small stone dungeons scattered through the Black Forest, the ones with skeletons guarding the entrance. Inside, cores sit mounted on stands along the passages, glowing so you can spot them from a distance. Grab every one you pass.
The skeletons keep coming while you explore, so bring a 
Club or a mace. They resist arrows, and swinging blunt at them is faster than fencing with them.
One decent chamber usually covers your smelter and kiln. Two or three set you up for portals as well.
Source two: surtlings, the endless supply
Surtlings are the small fire creatures. You will meet a few around fire geysers in the Black Forest, and far more in the Swamp, where geysers spawn them constantly. Every kill drops cores, and unlike chambers, this never runs out.
The trick that makes this effortless: surtlings die on contact with water. Dig the ground around a swamp geyser down a little so it floods, and everything that spawns kills itself. You come back every so often and sweep up the cores.
What to spend them on, in order
Smelter, 5 cores. No smelter, no metal.- Charcoal kiln, 5 cores. It feeds the smelter.
- Portals, 2 cores each end. Build these the moment you can spare the cores, they change the whole game. Recipe in the portal guide.
If you are short, the smelter and kiln come first. But do not stop collecting at 10, because you will want portals everywhere before long.
Happy hunting!
