If you've come to this guide it's likely for a couple of reasons. If you've just updated from MIUI 5 to MIUI 6 beta, you're likely seeing some weird force closes of Google Apps or just some other incompatibilities that didn't exist in MIUI 5. Maybe you may just be having general problems with Google Apps in MIUI, errors like "Google Play Services has stopped working" or "Gmail has stopped working". Thankfully this is a pretty easy fix, but it's going to erase any system data that you've got set up, so anything related to accounts, contacts, messages, etc. Your pictures and other personal data should still be fine, but just in case don't forget to back up your data before anything this involved just in case something goes wrong.
Getting started let's make sure to grab the latest Google Apps package for Mi phones here, specifically the "8-11_GApps_Standard_4.4.4_signed.zip" package at this time of writing. This is the latest set of Google Apps made specifically for MIUI phones, and should work just fine on both MIUI 5 and MIUI 6 no matter which Xiaomi phone we're talking about. Once you've got this file downloaded onto your phone navigate to the file explorer app that comes with your device (or your favorite one if you prefer another), and rename the file to "update.zip". Be sure to make the name all lower case and double check the spelling. Once you've renamed it move it to the top-most directory of your phone (the root directory) by cutting and pasting the file.
Now you'll need to reboot into recovery mode in order to install the updated Google apps file, so hold down the volume up and power buttons until the phone restarts, and continue holding them until you see the Mi logo and the logo brightens up. Once you're in recovery mode you can navigate the menus by using the volume up and down buttons, and pressing the power button works like an enter button. Select your language (likely English if you're reading this) and then head down to "install update.zip to system" and select it, then press yes to accept the installation. This should be a fairly quick installation and should only take a few seconds. Once it's done click OK, then head back to the main recovery menu.
From here we'll need to wipe cache and user data to ensure nothing got mucked up in the flashing process, so click on the second menu item down labeled "Wipe & Reset". From here you'll need to do both "Wipe Cache" and "Wipe User Data" to clear off any previously configured data. Once you've completed both steps use the reboot menu option and select the option that's labeled "latest". The phone will take a little while to boot up because it's essentially booting as it did for the first time, and you'll have to go through all the initial setup like logging into your Google and Xiaomi accounts, etc. From here all the weird force closes and other issues found with Google apps should be gone, and you can use the Play Store and all the other great Google Services that you're used to having on other Android phones. If you don't have your own Xiaomi Mi4 you can buy the 16GB version here, and the 64GB version here!