What I did to get from working GPG to green and verified signatures for Git commits and tags on GitHub.

1. Find the long id of the Signing key we want to use:
   🔶 > gpg --edit-key alice
   gpg (GnuPG) 2.0.30; Copyright (C) 2015 Free Software Foundation, Inc.
   This is free software: you are free to change and redistribute it.
   There is NO WARRANTY, to the extent permitted by law.
   
   Secret key is available.
   
   pub  4096R/AA79CCAE  created: 2017-08-23  expires: never       usage: SC
                        trust: ultimate      validity: ultimate
   sub  4096R/62275E24  created: 2017-08-23  expires: never       usage: S 👈
   sub  4096R/4AEA9524  created: 2017-08-23  expires: never       usage: E
   [ultimate] (1). Alice Person (alice) <alice.person@example.com>
   [ultimate] (2)  Alice Person (alice) <alice@example.org>
   
   🔶 gpg> quit
   
   🔶 > gpg --list-secret-keys --keyid-format LONG alice
   sec   4096R/8C0BBECBAA79CCAE 2017-08-23
   uid                          Alice Person (alice) <alice.person@example.com>
   uid                          Alice Person (alice) <alice@example.org>
   ssb   4096R/6ADB9D4262275E24 2017-08-23 👈
   ssb   4096R/33F2E1644AEA9524 2017-08-23

   Note: So in this case we want 6ADB9D4262275E24

2. Configure git and (optionally) make it sign commits and tags by default:
   🔷 > git config --global user.name "Alice Person"
   🔷 > git config --global user.email "alice.person@example.com"
   🔶 > git config --global user.signingkey "6ADB9D4262275E24"
   🔷 > git config --global commit.gpgsign true
   🔷 > git config --global tag.forceSignAnnotated true
   🔷 > git config --global push.gpgsign if-asked
   🔶 > where gpg
   C:\Program Files (x86)\GNU\GnuPG\pub\gpg.exe
   🔶 > git config --global gpg.program "C:/Program Files (x86)/GNU/GnuPG/pub/gpg.exe"
   🔶 > echo no-tty >> %APPDATA%\gnupg\gpg.conf

   Note: If repo specific, just skip --global and run the command in the repo instead.

Test it…

3. Do a commit:
   🔷 > git init gpg-test
   🔷 > cd gpg-test
   🔷 > touch file.txt
   🔶 > git commit -a -m "Signed commit"
   [master (root-commit) 2814856] Signed commit
    1 file changed, 0 insertions(+), 0 deletions(-)
    create mode 100644 file.txt

   Note: If not using commit.gpgsign true, one can also use -S to explicitly sign a commit.

4. Verify commit was signed:
   🔷 > git log --show-signature
   commit 2814856365a07b3deb374f1337258102c06b77ef
   gpg: Signature made 08/23/17 06:18:50 W. Europe Daylight Time^M
   gpg:                using RSA key 6ADB9D4262275E24^M
   gpg: Good signature from "Alice Person (alice) <alice.person@example.com>" [ultimate]^M
   gpg:                 aka "Alice Person (alice) <alice@example.org>" [ultimate]^M
   Author: Alice Person <alice.person@example.com>
   Date:   Wed Aug 23 06:18:48 2017 +0200
   
       Signed commit
5. Add a signed tag, using -s:
   🔶 > git tag v1 -m "Signed tag"

   Note: If not using tag.forceSignAnnotated true, one can also use -s to explicitly sign a tag.

6. Verify tag was signed:
   🔷 > git tag -v v1
   gpg: Signature made 08/23/17 06:34:18 W. Europe Daylight Time
   gpg:                using RSA key 6ADB9D4262275E24
   gpg: Good signature from "Alice Person (alice) <alice.person@example.com>" [ultimate]
   gpg:                 aka "Alice Person (alice) <alice@example.org>" [ultimate]
   object 53e7f2e637eaf3c47b5dcad30b57be7b6829be02
   type commit
   tag v1
   tagger Alice Person <alice.person@example.com> 1503462856 +0200
   
   Signed tag

Add GPG key to GitHub

7. Export the public key:
   🔶 gpg -a --export alice > public.txt
8. Copy it.
9. Go to GPG keys on GitHub.
10. New GPG Key.
11. Paste it.
12. Add GPG Key.
13. Pushed commits and tags should now look verified, as in this post: GPG signature verification…

Sources: help.github.com, StackOverflow, git-scm.com