Improving your TechPriests involves spending Blackstone. Blackstone is gained for finishing missions, but also from scanning necron consoles during missions, killing necron units, and as a reward for many glyphs and events during the game. Each time a TechPriest ranks up, the cost of ranking up again will increase, starting at just above 100, but increasing by about 30 for each rank. Blackstone is kept as a total pool shared by all TechPriests, so be careful about ranking one up far above another.
When you upgrade a TechPriest, that TechPriest will gain an additional augment slot, and unlock either a new skill or an additional piece of armour. Which skills are selected has a big impact on how a TechPriest will perform in combat, and what combat role will be ideal.