Whenever you are in a solar system, you can rightclick on the planets in your overview and click 'view in planet mode'. This will bring up a new menu, looking like the picture here above. It has two areas: 'manage' and 'scan'. You start with scanning, obviously, as you'll want to place your extractors where the resources are.
This first scan attempt, on a planet in Halle, didn't show much results; the planet surface doesn't show obvious locations where mineable resources might be found, even though the white bars indicate the resources should really be there somewhere.
A second scan attempt, in Uphene, yielded some results: the green areas contain deposits of heavy metals, so that's where I established my base. Here's the main control tower and two extractors.
These are placed from the 'manage' part of the Planet menu. You'll need to have control towers in your cargo hold, and the type should suit the planet you're exploring. There's different control towers for planetary surfaces: water, ice, lava, gaseous, temperate etcetera. I had the right type in my cargo hold, so I opened the Control Towers, and selected 'lava control tower'. Here's where it all gets a bit counterintuitive: the Control Tower menu now closes itself, and you have to click on a place on the planet to actually place the tower. After you've done that, you need to click 'submit' which is at the bottom of the planet menu, and sometimes obscured by the chat window!
Placing the extractors works the same way - but you don't have to have them in the cargo hold. Supposedly they are available in the command tower. The extractors do the actual digging, and you'll want those on the most rewarding locations on the planet. You have, again, to open the relevant part of the Planet menu, and select the type of extractor suitable for the stuff you want to extract:
Here's a closer view of my lava base. On Singularity, zooming in too much on a base results in an awful lot of lag, even when you're alone in a system.
After you have placed a control tower and some extractors, you need to link them; the control tower needs to provide the extractors with energy and computing power. Here I'm establishing a link between my main control tower and a new processing plant. Oh - don't forget to click 'submit' after every step or it won't work.
Of course, the extractors need to be instructed to do the actual extracting. If you doubleclick on an extractor, a menu appears:
The left icon with the arrow pointing down is the one used to start surveying for the extractable planet goo. The survey results can be selected for extracting.
After you've established links, you can use those to route the extracted materials to other parts of the facility, for instance the processor plant, the storage facility or the spaceport. The blue lines indicate links (which also feed energy from the control tower to the other facilities), the red lines indicate routes.
This is one of the extractors, it has already dug up some useful ore for me.
Here's where we stopped yesterday. Of course, the next steps are routing the extracted ores to a processing plant to create goods for sale, and have the space port send those goods off to space where you can retrieve them. When time allows, I hope to explore those areas too.