I've been asked several times now how one can get a verified copy of F-Droid. So here's a simple step by step explanation.
Please note that F-Droid recommends to install privileged extension. It enables a seamless app installation and update experience. So installing the APK only makes sense when you can't install F-Droid privileged extension.
Start out by getting F-Droids signing key:
gpg --keyserver keyserver.ubuntu.com --recv-keys 802A9799016112346E1FEFF47A029E54DD5DCE7A
Next let's get the apk and signature file:
wget https://f-droid.org/FDroid.apk wget https://f-droid.org/FDroid.apk.asc
now, lets verify it:
gpg --verify-files FDroid.apk.asc
Great, it's verified now you can use Bluetooth, ADB or whatever to copy/install the APK to your phone.
Of course this is just fetching everything from the internet. So it's essential to really make sure you've fetched the correct key.