In order to claim something, it can't already have an AI on it. If there is already an AI on it, you will need to destroy the previous AI first. Once there is no other AI on planet/space station, you only need to drop it on a tile, and you will claim it!
Once an AI is placed, you can right click on it and you will see a 'Manage' button. I've highlighted that below in green. Click Manage, then off to the right in the blue highlighted section, you will see a 'Show' button. Click the 'Show' button and you will see the full box in the highlighted blue section.
You can select from a list of rules that the AI will enforce. The AI will use energy to enforce these rules. AI slowly generate energy. A lone AI slowly gain energy up to 200. Which is not enough to properly protect itself, enforce your rules. In order to be able to store more energy, you will need to build AI Batteries to increase energy storage by 20,000 for each AI Battery.
AI Cores Allow your AI to spawn stronger and stronger monsters to deal with any issues it has responding to threats that violate the rules you set. Currently only 1 AI Core will actually do anything, there aren't monsters beyond the AI Edifice for it to spawn yet.
In the image above, I'm showcasing a basic AI setup that can effectively protect a low value target from most players. Many things are planned in terms of expanding AIs in Space Abyss!