The spell Shield does exactly what it says.
Until the start of your next turn, you have a +5 bonus to AC, including against the triggering attack, and you take no damage from magic missile.
There are no dice to roll.
Now if we look back at "Range" on p. 22 of the Starter Set Rules, we'll see that Shield is specifically mentioned when describing a spell that targets "self." This means that the effect does travel with the caster. Wherever the caster is (for the duration), there is the shield.
Historical note: Shield is explicitly an antidote to Magic Missile. In the early days it was pretty tough being a Magic-User at low levels, to the extent that you spent a lot of time just tagging along behind some meatier party members trying not to get in the way. But Magic Missile was the one thing you had going for you: it just hits. No to-hit roll, no saving throw. Boom.
Unless the target had Shield, which explicitly counters Magic Missile's unique ability. (There are other things than can eventually protect you from a magic missile, but at 1st-level it makes sense to look at them as a pair.)