For example, वह लड़की चली, फिर दौड़ी, और फिर गिर गयी। - That girl walked, then ran, and then fell down.
Good explanation. Just out of curiosity, why doesn't गिरना translate as गिरी in the example you gave?
Good question! You've asked about something that I think is the most idiosyncratic feature of Hindi. Alright. The last verb in my example (गिर गयी) belongs to the class of compound verbs. These are heavily used in Hindi and other Indo-Aryan languages and are common in Dravidian languages as well.
In Hindi, a compound verb consists of a verb root that conveys the actual action followed by another verb that adds subtle nuances to the overall meaning without drastically changing the literal meaning of the whole verb. There is only a handful of verbs that occupy the second position in a compound verb (e.g. common: जाना, लेना, देना; less common: डालना, पड़ना, आना, बैठना, उठना, etc.) and it's only the second verb that undergoes declension; the first one always occurs as a verb root. These verbs never occur in the progressive aspect. Here are a few examples:
(Translations are approximate so take them with a pinch of salt)
मेरा कबूतर उड़ गया (~fly-went) - My pigeon flew away (Compare उड़ जाना (to fly away) with the non-compound form उड़ना (to fly)).
भाग जाना (~run away-go) - To flee (भागना - To run away).
सो जाना (~sleep-go) - To fall asleep (सोना - To sleep).
वह रो पड़ा (~cry-fell) - He burst into tears (रोना - To cry).
उसने मकड़ी को मार डाला। (~kill-put) - She killed the spider (मारना - To hit/beat).
तुमने क्या कर दिया! (~do-gave) - What have you done! (करना - To do).
अंडा घोंसले से गिर गया (~fall-went) - The egg fell out of the nest. ("गिर जाना" indicates something falling suddenly, unexpectedly. गिरना - To fall).
अंडा ज़मीन पर गिर पड़ा (~fall-lay) - The egg fell onto the floor. (गिर पड़ना emphasizes the contact between the falling object and the surface).
Some actions/events are almost always described using compound verbs.
To be lost/To go missing - खो जाना (The non-compound form is खोना (intransitive) and also means "to be lost" but it it's generally used with जाना).
My book has gone missing. - मेरी किताब खो गयी है।
To lose - खो देना (Non-compound form: खोना (transitive))
I've lost my book. - मैंने अपनी किताब खो दी है।
Finally, some frequently used and relatively hard-to-translate compound verbs:
आ जाना (~to come-go) - The simplest compound verb, आ जाना is used in reference to a quick, unexpected, or much-awaited arrival of someone or something.
आख़िरकार बारिश आ गयी। - Finally the rain has come.
मैं कल आ जाऊँगा। - I will come tomorrow (there is a tone of affirmation or reassurance here, unlike मैं कल आऊँगा, which is a plain statement).
कर लेना (~do-take) - To do something to or for oneself.
मैंने अपना काम कर लिया। - I've finished my work.
कर देना (~do-give) - To complete a task, do something quickly, accidentally, or commit something bad, etc.
रख देना - To put something somewhere (not in one's own pocket, mouth, etc. though).
सेब को मेज़ पर रख दो। - Put the apple on the table. (रख दो sounds more casual. सेब को मेज़ पर रखो may sound a bit authoritative. Also, रखना by itself can mean both "keep" and "put").
रख लेना - To take something and put it on oneself or keep it with oneself.
उसने किताब को अपने सर पर रख लिया। - He put the book on his head.
ये पैसे रख लो। - Keep this money (with yourself).
दे देना (~give-give) - To give casually, without delay, unhesitatingly, etc.
प्लीज़ थोड़ा खाना दे दीजिए। - Please give (me) some food.
ले लेना (~take-take) - To take quickly, casually, etc.
वह सबको खिलौने दे रहा था, एक मैंने भी ले लिया। - He was giving toys to everyone, (so) I also took one.
Note: The above explanations aren't exhaustive; the subtle meanings spanned by compound verbs are too diverse and the number of compound verbs themselves too vast to be thoroughly explained in a post less than ten times longer than this. Listening to Hindi conversations, news, songs and reading stories can be a great way to understand and acquire compound nouns.
That girl walked. - वह लड़की चली। This would probably only be used in reference to an instance or a short period of walking. For example, वह लड़की चली, फिर दौड़ी, और फिर गिर गयी। - That girl walked, then ran, and then fell down.
When "That girl walked" is used in the sense of "That girl used to walk", it would be translated as "वह लड़की चलती थी" or वह लड़की चला करती थी".
The verb जाना is an action verb much like “to go” is in the English language i.e. “I’m going to read a book.” A learner would ask, “what does planning to read a book have to do with going?” Here गयी is the down part of fell down. If “she fell” was all that you want to say then “वह गिरी” will suffice.