NMSResources Infographics

To start creating a base, simply place a Base Computer.

This allows you to build in a 300u area, extending out to 1000u (plus a bit) as you build.
Story missions award a large amount of base building parts for free.

You can buy those & the rest for buried salvaged tech on the Space Anomaly.

Things to consider before building:

Have you found a relatively flat piece of land to build on? Terrain edits are a pain.
Once you build your base computer, its exact location is fixed. Make sure you build it where you want it. See graphics below.
Are there S or A class power / gas / mineral hotspots around, as that's a massive bonus.
Do not build within 1000u of someone else's base / 300u of a portal, as this will lead to problems with your (and their) bases.
Building bases on community planets, such as the weekend missions, will always be subject to deletion by HelloGames. To avoid this, only build away from the portal & only build close to the anomalous region if your base helps with the mission in some way. Always keep these bases simple. Bear in mind that other people's systems have to load it all in.
On each planet, only the last base you uploaded will be visible to others (unless they are currently in your game).
Do not mix bases together. They do not share power & mess each other up.
Bases should always be uploaded. This protects your edits, both parts & terrain, as well as making your base visible to others. Once you pass 3000 parts, you can no longer upload that base.