I would like to know how to use the verb to be and its past participle.
The rain is gone.
Is is present perfect tense here?
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Nope. That is not present perfect tense. What you have there is a simple sentence whose verb "is" is in the present tense.
A present perfect tense follows the format:
has/have + past participle of the verb
eg. She has arrived
You can use the present perfect tense when you want to convey an action completed in the past, or extends to the present:
I have run 4 miles.
This means that you started running sometime in the past and at the moment you speak, you are 4 miles away from your starting point. You are also conveying that you are still running.
I have studied French
This one means that at some time in the past, you took French courses and finished them.
Also when you want to use the verb "to be" + the past participle, the past participle acts as a predicate adjective. See usage of participles: http://www.slu.edu/colleges/AS/languages/classical/latin/tchmat/grammar/whprax/w23pplex.html
Edited: Thanks to @tchrist for making me remember of an old usage of the word "to be" in present perfect". I am actually not aware of that structure so I did a little googling and it lead me to this video