Learn Icelandic: Ég ætla að fara til læknisins.

This happens because of the preposition til (to). In Icelandic, til forces the noun that follows it to be in the genitive case (often called the possessive case). For many masculine nouns like læknir (doctor), the genitive ending is an -s. You can think of it as literally saying you are going 'to the doctor's'.

If the basic word for doctor is læknir, where does the -sins part of læknisins come from?

The -sins is the definite article ("the") attached to the end of the word, shaped for the genitive case. Normally, "the doctor" is læknirinn. But because til forces the genitive case, both the noun and its attached article must change. The noun gets an -s (læknis) and the article becomes -ins, combining into læknisins.

Why do we need að between ætla and fara?

The word að acts just like the English word "to" when you connect a conjugated verb to an infinitive (dictionary form) verb. Because ætla means "intend", you need að to say you intend to do something. Therefore, að fara translates perfectly to "to go".

Can I translate Ég ætla að fara as "I am going to go" or "I will go"?