With apologies to the wiki: Why do CCP always make pages that can't be read ingame?

How do I increase my ship's powergrid?

The best method is to study the engineering skill, which will increase the powergrid of every ship you fly by 5% per level. You can also fit a power diagnostic system or a reactor control unit, or for a frigate, a micro auxiliary power unit.

How do I increase my ship's CPU?

The best method is to study the electronics skill, which will increase the CPU of every ship you fly by 5% per level. You can also fit a co-processor.

How do I increase the cargohold capacity of my ship?

For certain ships, like industrials, simply increasing your piloting skill (e.g. Amarr Industrial) will increase your cargohold size. You can also install Expanded Cargohold modules in your lo-slots or, for richer players, Cargohold Optimization rigs. Finally, if you have over 3,000m3 of cargohold size, consider keeping a Giant Secure Container in your cargohold: they are 3,000m3 in size, but they will hold 3,900m3. This is a 30% increase when carrying small items, but don't do it if you want to carry items larger than 3,900m3.

What are upgrade hardpoints?

Upgrade hardpoints are used to fit rigs, which can be found in the market under the category 'Ship Modifications'.

How do I increase my drone hold size/launcher hardpoints/turret hardpoints/ship fitting slots?

You can't. Buy a better ship.