There are three general ways to achieve a galactic victory in PlanetWars.
Conquering an enemy homeworld - *any* enemy homeworld - grants the victory to the conqueror. The faction that lost their headquarters will have more drastic consequences to their lore, but every other faction besides the conqueror loses as well.
This is the most straightforward method, but also the most difficult. Homeworld planets come with massive defensive bonuses and are protected from warp and influence projection (though not from massive bomber and dropship fleets).
As an alternative to the costly siege, it is possible to simply blow up an enemy homeworld using a Planet Buster or a Galactic Compressor. For this reason, any faction that has managed to save enough metal to build a Planet Buster, and enough power infrastructure to feed it, can be assumed to have won the game -- as long as they can protect the superweapon while it powers up.
Some planets come equipped with indestructible, energy-demanding, Ancient Artefact structures. These can be activated with a sufficiently massive power infrastructure, upon which they will generate Victory Points each turn. The first faction to accumulate 100 Victory Points, wins - unless someone wins faster using the other methods. Artefacts take time to power up, and while indestructible on the galaxy map, can be destroyed in battle to deactivate them for several turns.