1. download: you can also get clean downloads from apkmirror.com and apkpure.com
2. verify: make sure you didn't download malware. the 3 linked sites all offer a clean app download, and the malware infected ones are probably just floating around some shady forums, but just to be sure:
2.1 find out the Pokemon Go apk hash (usually md5 or sha1)
look for some hash that is posted on some other, unrelated website (e.g. if you download from apkpure.com, don't necessarily trust the hash that apkpure.com tells you)
2.2 check the hash of your downloaded apk. You can easily do that with an online tool such as onlinemd5.com
2.3 make sure that the hash matches the one we found in step 2.2
3 how to enable installing apps from outside the Play Store:
(on older android phones, it's not under Applications instead of Security)
4. installation: download/copy the file onto your phone and open it. Install as usual
NOTE: check the permissions the app is requesting when installing! if something is unusual, such as recording audio or sending SMS, make sure you got a safe apk! (see blog post below*)
5. revert settings: (optional) uncheck "Unknown Sources" again (see step 3)
* post about pokemon go malware: http://gizmodo.com/did-you-install-this-malicious-pokemon-go-app-1783399021
This is a good guide, I think it would be a good idea to have the checksums for each of the apks you point to (with their respective versions) .
This is what I get from the apkpure site for version 0.29.3:
d65ea6e2929f0c67dbf6a8886b926fe6
And I get this from apkmirror for version 0.29.0
2580d2687af1ffaaec16ff3b48380f76
APK police confirm the apkpure hash for me, and the screenshot you have on your guide confirms the apkmirror version.