Learn German: Der Doktor hat mir eine Tablette gegeben.

In German word order, when you have both a dative object and an accusative object, a pronoun almost always comes before a noun. Here, the dative pronoun mir (to me) naturally comes before the accusative noun phrase eine Tablette (a pill).

Why do we use mir instead of mich?

The verb geben (to give) takes a dative object for the person receiving the item, and an accusative object for the item being given. Since you are the receiver, you must use the dative form mir instead of the accusative mich.

Could I say eine Pille instead of eine Tablette?

You should be careful with that! In German, eine Tablette is the general word for a medical pill or tablet (like aspirin or antibiotics). The word die Pille is almost always understood as the contraceptive pill.

Why does the past participle gegeben end in -en instead of -t?