Notice that you have a lone pair of electrons present on the nitrogen atom. Now, a hydrogen ion, H+ , which essentially is a proton, will be attracted to that lone pairs of electrons. The bond that is formed when a hydrogen ion is attached to the ammoniamolecule is called a coordinate bond (or a dative covalent bond).
The nitrogen atom donates its lone pair of electrons to form a coordinate bond with the proton. These two electrons are now bonding electrons between nitrogen and the fourth hydrogen atom in NH+4.