Technospire is a turn-based game - everytime your ship moves, attacks or uses an ability, all enemy ships can do so as well. The rooms in the Technospire can contain various traps, which activate every so often. Keep track of their patterns so you can avoid moving into traps.
When you defeat enemy ships, they might drop a boost. Certain boosts can repair your ship or grant you energy, others give you a temporary bonus or lower the cooldowns of your abilities.
Use the shape of the rooms to your advantage : lure enemy ships into doorways or small passages so you don't have to fight multiple ships at once. If enemies spot you, they'll try to move towards you, unless you stay out of their sight for a few moments. Enemy ships are immune to the effects of traps and turrets.

Playing a level for the first time gives you 100% chance that one of the ships in that level drops a datacube, which can be used to improve the stats and abilities of your ship.
Playing a level again has a 50% chance of giving you a datacube, but once you have completed a level, you may turn on additional difficulty options that either increase the number of ships or the number of traps on a map (or both). Doing so increases the chance of a datacube being dropped on this level.
Completing a map for the first time also awards an extra datacube.

The skills screen allows you to invest the datacubes you have aquired into a number of passive an active abilities. Improving any ability also grants a boost to your ship, be it damage, hitpoints or energy.
Passive abilities don't require any energy, while active abilities both require energy and have a certain cooldown before they can be used again.

Pages on the NULLL forum :
Technospire forum

Wiki pages:
Overview
Screenshots & more