How does Latias move?

Assuming that you are talking about the Pokemon Latias, the question can be ed in two ways.

The first is literal. Latias is a part Psychic-type Pokemon. It is in Psychic-type nature to defy gravity and give the illusion of flight. Latias moves by emitting a psychic field around herself, giving her the ability to float. Folding her arms close to her body, Latias may 'fly' faster.

Of course, you could very well be asking about the pattern of Latias' movement in the game. This is an entirely different question if so. Latias moves about the Hoenn region after you defeat the Pokemon League. Her movements about the region are random but have some patterns to them.

Firstly, you will notice that Latias will move to the opposite side of Hoenn to you if you fly somewhere. I suggest that if you want to capture her, you refrain from flying. Latias does not descriminate on which land she occupies. This means that, except for caves, Latias may be found on the ocean or in the grass. Places where there are neither makes it impossible for encounter as you need one of the two to see a Pokemon anyway.

Latias will always shift which route she occupies everytime you yourself change routes or when you enter or exit a building. This is actually very handy. If you repeditively enter and exit a building right next to a patch of grass, there is a chance you will meet Latias there. This means you do not need to go to her, she comes to you!

You should also note that Latias will almost always move to the route next to her previous one. For example, if she occupied Route 125, then her next route will be 126 or 124 - unless you use Fly.

Besides the points given above, Latias' movement is random. I have not seen sources that suggest otherwise and I doubt Nintendo would make the movements very predictable. It is in the game's history to make capturing difficult.