How can we download paid Android apps for free in a legal manner?

There are very few ways to get a paid Android App legally for free. These are:
1. Amazon App Store - Amazon gives a paid game or app for free everyday. But it doesn't mean we will get an app of our choice. The free app is randomly selected by Amazon itself. So there is a trillionth chance of not getting the desired app.
2. Ad Supported Version - Sometimes developer also creates a free version of a paid app with inbuilt ads support. So checkout for an Ad supported version of the Android App via different app store like Google PlayStore, Amazon App Store, Opera Mobile Store and Getjar etc.
3. Try Alternatives - This is the last but a very reliable option. Search free alternatives of a paid app. You will surely get a free alternative app of your favourite paid app.

There are a few ways to get paid Android apps for free legally-

Using the app AppGratis : Download and install the app. It offers you one paid for Free everyday. Apart from that there are multiple deals on other apps as well.

Using the app Amazon Appstore: Install Amazon app store on your phone. You can be assured of getting one paid for free everyday - under App of the day offer. Who knows, your favourite app may land In there one day

Using the Amazon coins: Amazon app store provides Amazon coins on purchase of some paid apps.  You can purchase apps of your choice using these coins for free or at a discount.

Taking Google Play survey: Take Google play surveys. Once your earnings accumulate, you can use the credits to buy the app from Play store.