Problem: you got a phone or tablet without Google Play, so, it is hard to download apps. There are other apps servers (Amazon, for instance, or the website of the app vendor or Getjar, although the last one is more risky) but many times, Google Play is the only way.

Solution if you have the .apk (the distribution file with the application):
  1. With the USB cable, place it in the directory Download.
  2. Move to that directory within your phone or tablet and open the file. It will ask you if you want to install it. If you don't have a way to browse to that directory, go to point #5 below.
If you don't have the .apk file, here is an alternative method:
  1. Download whatever you want with the tablet that has Google Play (we will call this tablet, tablet #1). Or if you now somebody who already has the app on their tablet, move to step #2.
  2. Install Antro File Manager in tablet #1. To the right, there is a backup option. Do that for the app that you want and it'll be in SDCARD/backups/apps.
  3. Install and FTP server in tablets 1 and 2 (the one without Google Play). Suggested apps are Rapfox or Swiftp. (For tablet #2 you can use Amazon Store to get that app). Also you may want to try simply the USB cable for the next steps, instead of the ftp...
  4. Copy using the ftp ("get") the backup of the app from tablet #1 to PC and then upload ("put") to tablet #2.
  5. Install a file manager like ES File Explorer in tablet #2 (again, you can get it from Amazon store or Getjar).
  6. In tablet #2, go to the directory where you put the app and install it.
There may be ways to skip tablet #1 all together and download the apk straight to the PC, but have not looked for them...