Learn Farsi: دانشجوهای تحول‌خواه میرن راهپیمایی. - The progressive students are going to the rally.

تحول‌خواه is made by combining the noun تحول (change, transformation, or evolution) with the suffix -خواه. This suffix comes from the present stem of خواستن (to want/seek). Literally, a تحول‌خواه is a "change-seeker," which perfectly captures the meaning of "progressive" or "reformist" in a political or social context.

Why is there an extra ی in دانشجوهای before the next word?

The word for students is دانشجوها (using the plural suffix -ها). Because we need an ezafe to link the noun to its adjective (تحول‌خواه), and دانشجوها ends in the vowel alef (ا), we must insert a glide consonant ی (y) before adding the ezafe vowel. So it becomes دانشجوهای (dâneshju-hâ-ye).

The translation says they are going "to the rally", but there is no word for "to" in the sentence. Why?

The verb میرن (a colloquial, spoken form of می‌روند, "they go") is a verb of motion. In everyday spoken Farsi, the preposition به (to) is frequently dropped before the destination. So, instead of saying میرن به راهپیمایی, native speakers usually just say میرن راهپیمایی.

What are the building blocks of the word راهپیمایی (rally)?

It is a compound noun. راه means "path" or "way", and is the present stem of the verb (to traverse). The at the end turns it into a noun describing the action. So, literally means "path-traversing" or "marching," which is the standard word for a rally or demonstration.