Currently the only possible way to explain the behavior of the atoms, molecules and, up to a certain extend, condensed matter is to use the methods (solving Schrödinger equation) and principles (Pauli exclusion) of quantum mechanics. This means that one needs to write down the Hamiltonian of the system, that is, find out the interactions between electrons and nuclei (which is just attraction or repulsion between charges) and solve the Schrödinger equation.
The problem is that beyond two body system (H atom) Schrödinger equation is so complicated that we need approximations for solving it. Even for the simplest molecule ($H_2$) Schrödinger equation cannot be solved exactly. If you want to learn how to treat hydrogen molecule quantum mechanically have a look at, for example, this lecture notes from Introductory Quantum Mechanics I course at MIT.
So, after this general introduction let me try to answer your questions.
I made a google search and found your book online. You say
In my book it is given that for the formation of hydrogen molecules, hydrogen atoms come closer due to net attractive forces.
It is written that initially when the atoms were at distance the magnitude of attractive force was greater than that of repulsive force and hence they come closer and ultimately the system acquires a minimum energy state.
However in your book in the beginning of the discussion it is clearly stated that "Consider two hydrogen atoms A and B approaching each other...". So, two H atoms (being electrically neutral) far from each other (ignoring gravity) will not attract each other. But if one (somehow) brings them closer at a certain distance (always attractive) van der Waals interactions kicks in. But your book does not even bother with that that. The only confusing thing the book makes is to call the-one-and-only Coulomb forces as "new attractive and repulsive" forces. There is nothing new about them and they are the only forces in action, at any time.
I took the image below from your book. This image is pretty clear and this potential curve is known as Lennard-Jones potential. Keep in mind that the real thing is solving Schrödinger equation and Lennard-Jones potential is an approximation.
What this images says is that when two atoms are far away there is (essentially) no interaction between them but as they come closer there is an attractive force (van der Waals and/or Coulomb) and therefore a minimum at the potential well and this is the length of the bond between the two atoms. If one keeps decreasing the distance they start to repel (Pauli exclusion and/or Coulomb) each other.