a tenant rents, the landlord...!

[Jraou]

Hi there,

A tenant rents a house, then what does the landlord do in this case?

[Molly]

Lets.

[Yankee]

Hi Jraou

In AmE, a tenant can rent a house from someone, or a landlord/owner can rent a house (out) to someone.
Using your specific wording, I might say "a tenant rents, the landlord rents out".
http://www.merriam-webster.com/dictionary/rent%5B2%5D
.
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[Jraou]

Thank you Molly; thank you yankee.

[Molly]

[Skrej]

Of course we have the word 'let', but it's not used in terms of renting/leasing in AmE. It's listed as 'chiefly British' in the dictionary.
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[Molly]

[Jraou]

[Diverhank]

rent and lease are almost the same but they are different enough not to use one word. You use rent/lease together to express the general act of renting/leasing (there, I just did it myself).

[Yankee]

Here is an example of how I'd use "rent" and "lease" differently:

I might say "I rented a car at the airport" if my use of the car was short-term (e.g. for a week).

I might say "I leased a car" if I planned to use the car on a long-term basis (e.g. a year or longer).

If someone rents a house at the beach for two weeks, they generally have to sign some sort of rental agreement. If someone rents a house long-term, then I think the agreement that is signed is more likely to be referred to as a "lease" (although I wouldn't rule out the use of the term "rental agreement").
.
_________________
"Nearly all men can stand adversity, but if you want to test a man's character, give him power." ~ Abraham Lincoln