Learn German: Wir ziehen uns die Schuhe an. - We are putting on our shoes.

In German, when talking about body parts or clothing, you usually don't use possessive words like 'my' or 'our'. Instead, you use a dative reflexive pronoun (here, uns) to show whose body it is, and a basic 'the' (die) for the item. You are literally saying 'We put the shoes on for ourselves.'

Is the reflexive pronoun uns in the accusative or dative case here?

It is in the dative case. The direct object being put on is the shoes (die Schuhe), so that takes the accusative case. The person receiving the action (putting the clothes on themselves) takes the dative case. For wir, the accusative and dative reflexive forms both happen to be exactly the same: uns.

Why is the word an sitting at the end of the sentence?

The verb in this sentence is anziehen (to put on), which is a separable verb. In a normal main clause, the prefix (an) splits off and moves to the very end of the sentence, while the core verb (ziehen) stays in the second position.

I learned that ziehen means 'to pull'. How does this mean 'putting on'?

While ziehen on its own does mean 'to pull', adding the separable prefix an changes the meaning entirely. anziehen is the standard verb used in German for getting dressed or putting on items of clothing.