For Ubuntu 12.04, these are the steps:
1. Install packages: gnupg libgpg-error-dev libassuan-dev
2. Download GPGME library from ​http://www.gnupg.org/download/index.en.html#gpgme
3. Extract, then run
   configure
   make && sudo make install
4. Install PECL extension
   sudo pecl install gnupg
5. Add to php.ini
   extension=gnupg.so

I tried followings on Debian Squeeze and it worked fine

apt-get install libgpgme11-dev
pecl install gnupg

create a new file under conf.d folder and add following lines 

; configuration for gnupg module
extension=gnupg.so

Reload apache configuration
/etc/init.d/apache2 reload 

Check PHP Info and you should see gnupg

Hope this helps.

To install on laravel sail:
<?php
sail publish
?>
Add to your Dockerfile:
<?php
    && apt-get update && apt-get upgrade -y \
    && apt-get install -y gcc-multilib libc-dev bzip2 libgpg-error-dev libassuan-dev \
    && apt-get install -y build-essential \
    && curl -sSn -o gnupg.tar.bz2 $GNUPG_URL \
    && mkdir gnupg \
    && tar -xf gnupg.tar.bz2 --directory gnupg \
    && (cd gnupg/gpgme-* && ./configure) \
    && (cd gnupg/gpgme-* && make && make install) \
    && pecl install gnupg 
?>
Add to your php.ini under [php]
<?php
extension=gnupg.so
?>
Finally:
<?php
sail build --no-cache
?>
Check you can see gnupg under modules when you run:
<?php
sail php -m
?>

For the folks in Debian Wheezy who are having a bit of trouble
heres a link to to a .deb file ( I use it ) for amd64 users

http://users.on.net/~cam.metzke/Debian%20Packages/Wheezy/gnupg/PECL-gnupg/

Anyway I built it for the community, hope it helps :)

Quick installation guide on Fedora 10:

Needed:
- c++ compiler
- php-pear
- gnupg
- libgpg-error
- gpgme
- gpgme-devel
- php-devel

Install with:
$ pecl install gnupg

Add an entry to /etc/php.ini:
extension=gnupg.so

Restart Apache > you're done.

On Ubuntu 20, this is provided via `php-gnupg` (or with a specific version `php8.1-gnupg`)

To install:

`apt install php-gnupg`

Here are instructions for how to resolve the issue where you encounter this error:

/usr/include/gpgme.h:80:2: error: #error GPGME was compiled with _FILE_OFFSET_BITS = 64, please see the section "Largefile support (LFS)" in the GPGME manual.

This is a result of the gnupg extension currently lacking largefile support. The solution is fairly simple.

pecl download gnupg
tar -zxf gnupg-1.3.2.tgz
cd gnupg-1.3.2

Open the file config.m4 in an editor, and add "AC_SYS_LARGEFILE" to a new line at the very end of the file, then save.

phpize
./configure
make
make install

Now simply add extension=gnupg.so to your php.ini, and the extension should work.

Hi - 

By default on Ubuntu 12.04 LTS gnupg needs to write to .gnupg in the home directory of the user running PHP (so for a web site this is www-data). You might need to make a ~/.gnupg for www-data and chown/chmod it correctly or everything will fail.

On Debian 5.05 (Lenny) I needed to install libgpgme11-dev

After spending so much time I could only install it on Linux and not Windows. There is very little instructions on the net about installation of this module, so I am going to write a small instructions that should help a straightforward installation on Linux without so much trouble.

Step 1: you will need a C++ compiler on your machine. For being sure try this command in the terminal:
<?php
sudo apt-get install g++
?>
Obviously you need GnuPG itself, so try:
<?php
sudo apt-get install gnupg
?>
Step 2: you will need "Libgpg-Error" downloaded and installed on your machine. 
2-1: Download the code from http://www.gnupg.org/download/#libgpg-error
2-2: Extract it to a directory. In the terminal, change the directory to the Libgpg-error directory.
2-3: Configure the package for building and installation with below command:
<?php
./configure
?>
2-4: In the same directory make it with below command:
<?php
sudo make
?>
2-5: In the same directory install it with below command:
<?php
sudo make install
?>

Step 3: you will need "GnuPG Made Easy" (GPGME) downloaded and installed on your machine. Some sources will tell you that you can "apt-get install" it, but actually you cannot. So do it like the latter:
3-1: Download the source code from http://www.gnupg.org/download/#gpgme
3-2: Extract it to a directory. In the terminal, change the directory to the GPGME directory.
3-3: Configure the package for building and installation with below command:
<?php
./configure
?>
3-4: In the same directory make it with below command:
<?php
sudo make
?>
3-5: In the same directory install it with below command:
<?php
sudo make install
?>

Step 4: Given that you have a LAMP server already and have php installed, you will need "pear" and "php source codes". To add them use below commands:
<?php
sudo apt-get install php5-dev
sudo apt-get install php-pear
?>

Step 5: Now you can install GNU Privacy Guard for php using PECL command:
<?php
 sudo pecl install gnupg
?>