The Lightning springs from your hand for delivering a shock to a creature which you try to touch. So make a melee spell attack against the target. You basically have advantage on the attack roll if the target is wearing armor made of a metal. So, on a hit, the target would take 1d8 lightning damage and also it can not take any reactions until its next turn starts.
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At Higher Levels:
Actually, at higher levels, this Shocking Grasp 5E spell damage increases by 1d8 whenever you reach 5th level the damage will be 2d8, 11th level 3d8, 17th level 4d8.
Attributes Of DnD 5E Shocking Grasp
|Casting Time||1 action|
|Target||A creature you try to touch|