Learn Farsi: لپ‌تاپ از گوشی گران‌تر است اما خودکار ارزان‌تر است. - The laptop is more expensive than the phone, but the pen is cheaper.

You add the suffix -tar to the end of the adjective. In this sentence, گران (geraan - expensive) becomes گران‌تر (geraan-tar - more expensive), and ارزان (arzaan - cheap) becomes ارزان‌تر (arzaan-tar - cheaper).

Why is the word از (az) used for "than"? Doesn't it mean "from"?

Yes, از (az) is the preposition for "from", but it is also used for "than" in comparisons. The Farsi structure for comparing two things is literally "A from B more-adjective is". So, لپ‌تاپ از گوشی گران‌تر است translates word-for-word as "Laptop from phone more expensive is".

In the second half of the sentence, why isn't there an از (az) after خودکار (pen)?

Because we aren't explicitly stating what the pen is cheaper than right there. Just like in English ("but the pen is cheaper"), if the object of comparison is already understood from context, you can just drop the از and use the -tar adjective on its own.

Does the word for phone, گوشی (gooshi), relate to the word for ear?

Exactly! گوش (goosh) means "ear", and adding the -i suffix turns it into گوشی, which is the most common everyday word for a mobile phone or telephone handset.