To keep your ship afloat when exploring new sectors, your best bet is to find allies, for example by joining a union, or working for a company. They might provide security for you if things go south, but often want something in return. If you are on your own, you have to hope for luck with the dice.
The core rules are straightforward: when you want to accomplish or avoid something, for example forcing open an airlock, or resisting the effects of strange radiation, you roll a d20 modified by the relevant ability and hope to roll 12 or more.
To increase your chances of succeeding, you can spend a void point. These points are gained from failed rolls and can also be used for other things, such as activating cosmic mutations – strange powers representing physical manifestations of the void.