If multiple forces act on an object, opposing ones are going to either cancel each other out or one force will overcome the other, and consequently there will be a total force in one direction. In every system, there is a net force, or total force in every direction, after accounting for forces canceling each other out and overcoming each other. You do this by summing the forces, and adding or subtracting the individual forces imposed on the object.
In static systems, every force acting on the object is cancelled out by an opposing force. This causes the object to have a net force of zero newtons. Say a 5 N force is applied to a 10 kg object towards the negative y direction, and a 5 N force is applied to the object in the positive y direction. The object will experience a net force of 0 N in the y direction.
For your example, in dynamic systems, an object will not have a net force of zero newtons. The individual opposing forces do not cancel each other out, but one overcomes the other by have a larger magnitude. Using the example from before, if a force of 5 N is applied to the same object pushing it in the positive x direction, and a force of 2 N is applied towards the negative x direction, the net force is 3 N towards the positive x direction.
Given these numbers, the 10 kg object will experience a net force of 3 N to the positive x direction. You can then use Newton's second law, Force (N)= Mass (kg) x Acceleration (m/s2) to find the acceleration of the object to be 3/10 m/s2.
Some questions may give you the net acceleration instead of net force, but its the same process. Sum the accelerations just like you would sum the forces, plug the numbers into F=ma, and you find the unknown- in this case, the force.