Answer:
Let's start with Newton's laws:
First Law: A body will remain at rest or in motion in a straight line unless acted upon by a force.
Second Law: Change in motion is proportional to the applied force and parallel to it.
Third Law: To every action, there is an equal and opposite reaction.
Usually, when you are in the earth, the third law is hard to see, this is because when, for example, you throw a ball, the force that the ball does to you is not comparable with the force that the gravity is doing to you, and maintaining you in place. But in the space, you don't have this force "protecting" you, so if you throw a ball in zero gravity, you will be impulsed in the opposite direction at where the ball is thrown.
Good ideas to have in mind when working in zero gravity are protection strings, that limit the distance that you can go outside the spaceship.
Having magnetized suits also can be very helpfull when working outside the ship, because it allows you to "glued" to it. (and for example, if you are removing out a screw, collecting this screw with some magnetic device would be necessary, because you don't want scraps of metal in the outer space, they can be dangerous)
Nowdays some spacesuits even come with small propulsors, that allow the astronauts to move with some control when they are working outside the spaceship.
For the task inside of it, there are a lot of problems, for example, the effect that the zero gravity has in your body, in how you can eat food and how you use the bathroom, and there are a lot of technological advances that simplify a bit the approach that astronauts need to take when doing these tasks.
Where maybe one of the most important, "non-technological" things you need to have in the spaceship, is a capacitated team that can bring a solution to different problems, like engineering problems or medical problems (and of course, al the equipment these specialist need to do it).