How do I install XDebug on docker's official php-fpm-alpine image?

The following is sufficient for simply installing xdebug on that image:

FROM wordpress:php7.1-fpm-alpine

RUN apk add --no-cache $PHPIZE_DEPS \
    && pecl install xdebug-2.5.0 \
    && docker-php-ext-enable xdebug

Building that and then running from a shell inside the resulting image produces the following:

$ php -i | grep Xdebug
    with Xdebug v2.5.0, Copyright (c) 2002-2016, by Derick Rethans

If you are concerned about image size you can remove the dependencies:

FROM wordpress:php7.1-fpm-alpine 
RUN apk --update --no-cache add autoconf g++ make && \
    pecl install -f xdebug && \
    docker-php-ext-enable xdebug && \
    apk del --purge autoconf g++ make

Great answer @msanchez_aplyca. Although more correctly removing the build dependancies via apk would be:

RUN apk add --no-cache --virtual .build-deps $PHPIZE_DEPS \
    && pecl install xdebug-2.5.0 \
    && docker-php-ext-enable xdebug \
    && apk del -f .build-deps