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Some people seem to have problems with this, so here are some tips how to capture different types of buildings:

Energy cores
(that is: power plants) can be captured in two ways:

a. First disconnect the enemy core from its power grid (by destroying the adjacent core or the transmitter which connects this core to the enemy Frame or to another core), then supply it with power from your own grid (by building your core close to it, or using a transmitter to transmit the power to it over larger distance).

b. Build your own core next to a working (connected) enemy core. Your core has to be so close that the perimeter shield (just shield in further text) raised by it, touches the enemy core. (In practice this means, you have to build your core at the edge of enemy core's paved ground or closer.)
If the enemy core's shield is active at the moment, you now have to wait that it becomes inactive (alternatively, see (*) below). When its shield is dropped, quickly raise your own shield (either the full shield or just the shield of your newly built core). This will disconnect the core from enemy grid and connect it to yours. You can drop the shield again immediately if you wish - the core is now yours. Of course the moment you do drop your shield, the enemy can do the same and use its shield to cut the core from your grid.

(*) If the enemy won't drop the core's shield for a very long time, there's a cheat you can use to still capture it: save the game and immediately reload it. Every time the game is reloaded, all shields are disabled and it takes a few seconds for the cores to reestablish them. If you are quick, you can raise your shield before the enemy does, and capture all its cores that your shield touches.
But beware: this can work the other way as well. If you aren't careful, the enemy can raise its shields before you, and capture your frames instead!

(**) This same trick also works if you want to quickly destroy an enemy core: usually as soon you start shooting at a core, enemy will raise its shield and repair the damage you inflicted, before dropping it again. But you can just fire a single volley, damage the core a little, save and reload, and voila - when the game reloads, the shield is down. So fire another volley, rinse and repeat until the core is destroyed.

Yeah, that is indeed cheating, but the game is quite hard - at times frustratingly so, and this cheat can save you a lot of time and frustration...

(***) Yet another trick (and this one isn't a cheat!): if you happen to be out of energy and cannot raise a specific core's shield, you can still force it up for a second (which is quite enough to capture the enemy core), by raising the entire perimeter shield. This can be a life saver at times.

Enemy Frame
You can only capture enemy Frame, when it isn't connected to any (not even one) energy core. In other words: you have to place your own core close enough to power enemy Frame, then destroy all enemy cores connected to it.
Plus, enemy Frame must not be installed (that is, it must float in the air - not touch the ground), otherwise your cores simply won't connect to it.

If it's installed (placed on the ground), you can force it to float, by disrupting the ground on which it stands. This can be done by any terrain-demolishing unit (e.g. Scummer, Extirpator, Scum Splitter, Piercer or the stationary Scum Destroyer). In principle you could also use crater-making bombing units (like Mortar or Howitzer), but these are more likely to hit the Frame itself than the ground beneath it, so better use the terrain-disruptors.

Other buildings
Any other buildings need to be disconnected from enemy's power grid and connected into your own in order to be captured.

It's not enough just to cover them with your shield (like capturing cores). In fact it can be quite dangerous if your own core is so close that it encloses an enemy gun (or unit) into the shield. Once inside your shield, enemy gun/unit can keep firing at your core, eventually destroying it.

That means, you have to capture or destroy the enemy core powering the building, before you can actually capture the building itself.

If the building touches the powered ground around enemy's Frame however, you cannot capture it at all, unless you force the Frame up in the air first! And be careful that the enemy Frame is still connected to at least one power core when it lifts up, otherwise you'll capture the Frame itself, instead of the of the other building!

There's a mission Inforb-1 (Emperor's Testament), where you have to capture enemy Electro Lab, while you mustn't capture or destroy the Frame itself. (Mission info actually says only: "Capture the strange laboratory", without specifying which lab that is. That got me stumped until I - more by chance than intentionally - happened to capture the Electro Lab).

There are no enemy power cores at all in the beginning. So if you manage to prevent enemy from building any cores (like I did), there's no way to capture the lab, without capturing the Frame first (which makes you lose the mission).
So beware.