- Don't take stuff you don't need - shields, armour, weapons all add to your mass, which reduces your jump range. You might want to start off with these and then sell them at the last station before you leave "the bubble".
- Apart from the frame shift drive, all the "mandatory" gear should be the smallest D rated component that will fit unless you can fit in a smaller A rated component. There's a button for this on coriolis.io but you usually need to make tweaks manually after you add optional modules.
- Get the biggest fuel scoop that will fit. It's worth hunting round for this before you set off, don't just accept the largest one that is available at the outfitting station you're at now. Fuel scoops are all zero weight.
- Try to do without a fuel tank. If you want the safety net, try to make the spare tank as small as possible.
- Buy the advanced discovery scanner and detailed surface scanner - the first means you don't need to hunt down distant objects using parallax shift, the second earns you more money on the objects you get up close to and (on undiscovered objects) gets you a 50% bonus and your name on the "First discovered by..." label.
- Buy as many auto field maintenance units as you can. Like the fuel scoop, they do not add to your mass.
- Prioritise what you bother to scan by how much it's likely to earn you.
The next few are the ones I discovered (pun intended) for myself, and are really only applicable to small-ship explorers. They may also be common knowledge, but I haven't seen them:
- Turn off your cargo hatch, sensors and power distributor. They aren't needed when exploring and only add to your fuel flow which comes out of your reservoir which is refilled by your main tank.
- Turn off your AFMUs for the same reason, and also so you can be picky about what you repair.
- Don't repair anything that you always leave turned off - don't forget that AFMUs need repair too, so if you feel the need for one, you should actually get two.
- If you're building your ship in coriolis.io or a similar site, disable modules that you will be switching off. It might allow you to go for a lower-spec (so perhaps lighter) power plant.
- Your fuel reservoir depletes continuously. You might not need to worry about that in a big ship, but in the little ones each segment of the main fuel tank display relates to one refilling of the reservoir. Bear this in mind if you're about to visit somewhere unscoopable and your reserve is low.
- If you need to step away for a long time but don't want to log off and lose your plotted route, get your supercruise speed below 1Mm/s and drop into normal space. If you turn off every module except life support and the power plant, you use a negligible amount of reservoir fuel.