Suppose we have a positively charged sphere in vacuum and another neutral sphere. The charged sphere creates an electric field. This field will be identical with that of a point charge. The field varies as inverse square of distance. The neutral sphere feels like it is placed in a uniform electric field that has a value same as that at the point due to the charged sphere. This electric field presence induces some charge on the left side of neutral sphere. The negative charges are pushed to the left side. This induces an electric field on the neutral sphere. But the electric field cannot penetrate through the sphere as it will violate Gauss's law. So the neutral sphere becomes oppositely charged that will produce an electric field that could counterbalance the incoming electric field at that point. This is to maintain an electrostatic equilibrium between the two spheres.
Whether positive or negative the charge, it will attract a neutral object.
Now if you need to find the induced charge on the neutral sphere, find the electric field due to charged sphere at the distance where the neutral sphere is located. We assume that the radius of the neutral sphere is very less compared to the distance of separation between the two spheres. Then you will get the electric field acting on the neutral sphere. Let's assume that our spheres are in vacuum. Then this electric field will be equal to the electric field developed by the neutral sphere as required by electrostatic equilibrium condition. The induced electric field will be opposite to the field at that point. From that value, and by using the electric field equation of a charged sphere, you can determine the charge on the neutral sphere.
When a charged object is placed near human, he will feel goosebumps. It is because, say, a positive charge is place near you. You are grounded. So since human body is a conductor, it carries negative charge from the ground to counteract that electric field. If you make contact with the charged object, the entire charge floes to the ground and the object becomes neutral.