You have to place the connection-rods on the ground, you can't attach them to buildings. If you have some in your inventory the rod will appear and you place it down. You have to place it in range (shown by the transparent rope that appears). You need compound to craft those rods.
Why won't tethers connect to base Astroneer?
Do you have an Oxygenator module installed in your base? Make sure the oxygenator (you can call down one for free right at the landing pad) is connected to the shelter (the starter one has an open slot for it) or a platform connected to the shelter.
How do you use an Astroneer Oxygenator?
To use a Portable Oxygenator, the player must first place it in one of the widget slots on the Backpack, then press the corresponding context key (default C or V, for left or right slot) to activate.
How do you unpack an oxygenator?
I don't want that. All right and I'm gonna pop that guy over here I'm gonna grab. This. Little starting table or a platform rather pop it up and I'm gonna pop the oxygenator. All in there there we go.
How do you connect Astroneer cables?
The player can also hold a cable, and press the context key to place the extender at the cable's end location, connecting the cable to it without having to connect it manually.
How do you place a tether in Astroneer?
If you have the compound you should see a greeen button just above the orange arrows you can click to create the tethers. Next, you press T to equip a tether and then use your mouse to position it and left-click to place it on the ground.