Covalent structure AlH4-

In [AlH4]^-, Al is covalently bonded with 4 H atoms, which requires 4 outmost shells electrons in Al to take place, however, we notice that there are only 3 outmost electrons in Al, thus 1 electron from others is received. (So you can notice there is 1- on the upper right-hand corner of [AlH4]^-)

In [NH4]^+, similarly, N is covalently bonded with 4 H atoms, which requires 4 outermost shells electrons in N to take place, however, we notice that there are 5 outmost electrons in N, thus 1 electron is lost to others. (So you can notice there is 1+ on the upper right-hand corner of [NH4]^+)

For the [AlH4]-, it can be consider as a complex ion form by an aluminium ion with 4 hydride ion as ligand. As the almuinium ion carry a 3+ charge and each hydride ion carry a -1 charge. To sum up, the whole [AlH4]- ion will carry a -1 charge

For the NH4+, it is formed a hydrogen ion attached to a NH3 atom. As the ammonia molecules is neutral in charge and the hydrogen ion is +1 ion charge, the whole ammonium ion will be +1 in charge