Google#
To create a Google Translate API key, you need a paid account. But the price of translation is very low – $20 per million characters. Due to its terms and services, Google does not allow unpaid use of their translation APIs.
Here is an example of translatepress to get the API key.
Yandex#
To create a Translate API key, you need an account. This provider allows to use their API for free with some limitations. Here is the key creation start point.