In Zero-G, all your attacks, Jump, and Tumble checks are at -4, unless you have Astrobatics. You cannot perform a Run action in space, but if you can fly, then you can move freely as if every direction were “lateral” movement (i.e., there is no up or down). However, if your ability to fly relies on being in an atmosphere (i.e., Wings) and you’re in the vacuum of space, then you’re out of luck.
If you can’t fly, you move in zero-G environments by pushing off of one fixed point and “landing” on another. For mundane movement, just floating around inside a ship for example, there’s no need to make any rolls. In combat or other dangerous situations in which timing is important, however, you must essentially throw yourself from one place to another, which requires either a ranged touch attack or Tumble check (player’s choice). You have a range increment of 30 feet and the DC for the attack/Tumble check equals the Defence score of the square you want to arrive on. An object or surface that takes up a five-foot square area has a Defence of 10, but a medium-sized object is Defence 14, a small object is Defence 18, and so on.
However, you do not automatically stop on a square. Instead, you have to land on a large surface or grab a fixed object to arrest your movement, which you can automatically do at the end of a single move action. If you take a double-move, however, you must make a Reflex save (DC equals 10 +2 per 10 feet of Tumble distance) to arrest your movement.
If there is nothing to grab on to in that square, then you keep moving, involuntarily, at your movement rate. Moving in this manner does not count as a move action because you expend no effort on maintaining your speed or manoeuvring around objects. You can, of course, use actions to try to arrest your movement.
If you find yourself in a low-gravity environment, as opposed to a zero-G environment, the easiest thing to do is apply the same -4 to Jump and Tumble checks. Assuming 0.5G (half of Earth’s gravity), you would Jump twice as high and you take half-damage from falling. You cannot Run unless you take the Astrobatics feet because you have to learn to travel with half of your weight, and thrown weapons and projectiles take a -4 penalty because they do not arc through the air in the same way, although firearms are basically unaffected.
If you want to get very specific about it, you can actually calculate all of these bonuses/penalties based on the amount of gravity present. For example, the Moon has 1/5th the gravity of Earth (0.2G), so your Jumps would be five times longer/higher (i.e., multiply by 5), and falling damage would be five times less (divide by 5). In addition, if you want to be precise, instead of applying a flat -4 penalty, you could apply a -1 for every 0.1G different from Earth, so the Moon (0.2G) would be a -8. Once you get lower than 0.1G, you are effectively in a zero-gravity environment, and those rules would apply.
If you find yourself in a high-gravity environment, you take a -8 to Jump and Tumble checks. Assuming 2G (double Earth’s gravity), you would Jump half as high and take twice as much damage from falling. You would have to calculate your speed based on adjusted encumbrance, as well. Thrown weapons and projectiles take a -4 penalty because they do not arc through the air the same way. High-gravity also halves the range increments of all ranged weapons, including firearms (e.g., if it’s normally 100 ft., in high-G it’s 50 ft.).
If you want to get very specific about it, you can calculate all of these bonuses/penalties based on the amount of gravity present. On a planet that has three times Earth’s gravity (3G), your jumps would be 1/3 as high and falling damage would triple. In addition, if you want to precise, instead of applying a flat -4 penalty, you could apply a -4 for every 1G different from Earth, so 2G would be a -4, 3G -8, 4G -12, etc. Range increments would, likewise, be divided by the G-rating of the environment: divide by 2 for a 2G environment, by 3 for 3G, etc. At a certain point, increased gravity makes you unable to move at all (i.e., when your weight exceeds your maximum lift), but well before that point, your own limbs would be so heavy that even lifting them to aim a weapon would be nigh impossible. If and when that happens, the GM is entirely within her rights to declare that you cannot make attacks at all any more.