I assume you're referring to the production core "base", as the factories are about as easy to take over as a normal city. If facing a core to the south, head directly south until the arrow starts to point back north. Then, move in the left or right direction until the arrow points directly upward. Take out any laser cannons along the way with your machine guns, as they're a pest and can be distracting. Move slowly to the north until you see the core moving around. Then, be patient and fire your missiles one or two at a time (depending on the type of missile). Watch the firing pattern of the core; it is very predictable and the timing gives it three distinct "phases" for when it shoots downward at you. If the core is initially to the north, it might be a good idea to go a little bit south to start so you can get the upper hand against the laser cannons, but the same strategy applies.
Knowing the firing time for your ATAC helps tremendously in terms of timing your attacks. For example: the Bile has a slow missile fire time, while the Blender fires immediately. For ATACs with slow missile firing times, you need to start the attack before moving into the direction you want to fire in. For immediate-fire ATACs, move in the direction and then fire. Also, note that not all ATACs fire from the center; some, like the Bile, fires from its top when fighting left/right and to one side when fighting up/down. Master the positioning of your firing when you do this. The best type of ATAC to take into the production units is an ATAC with a right-sided fire when shooting to the north.
The reason I mention the Bile so much is because it makes an excellent ATAC for storming production units when playing as Stefan. It has high HP and powerful missiles, even though its missile stock is a bit low. The Stormer is a great ATAC on Faliail's side for the same purpose. It is actually a better ATAC, with higher HP and greater firepower, plus it's all-terrain, so it can be used in space, unlike the Bile which is a Desert ATAC and cannot be used in space.
EDIT: Oh, and I should also mention that taking out the production units in space is a different matter. These are several times more challenging than the ones on planets. The cores move and fire faster and there are way more laser cannons to deal with.
EDIT2: Oh, and there's one HUGE exception to all of this, and it applies to playing as Falial in a space battle. Once you can get them (and they are very expensive), get a Reaper. These things are OPAF. You can literally tank a production core with these monsters in just a few seconds. They have overwhelming destructive power (40/4 iirc), insane defense, and the highest HP of any regular ATAC in the game. The downsides, of course, are that they are really expensive, and that they are Space ATACs so then can't be used in ground battles.