Yay, it's up and running! And here are the steps to do it, mostly copied directly from the shell as I ran them. In any case, it may or may not work for you, so make sure you check with the proper documentation if anything fails.

By the way: Back up old repositories if you have any!

  1. Install the software:
    sudo apt-get install apache2 libapache2-svn openssl ssl-cert subversion
  2. Create directory for server certificates:
    sudo mkdir /etc/apache2/certs
  3. Create password-free SSL certificate (remember what you put as "Host Name" for the next step):
    sudo /usr/sbin/make-ssl-cert /usr/share/ssl-cert/ssleay.cnf /etc/apache2/certs/server.pem
  4. Add the Apache certificate settings to /etc/apache2/httpd.conf (use the "Host Name" value from the previous step instead of "example.org" to avoid a warning in /var/log/apache2/error.log): 
    ServerName example.org
SSLEngine on
SSLCertificateFile /etc/apache2/certs/server.pem
  5. Enable Apache SSL module (necessary for HTTPS):
    sudo a2enmod ssl
  6. Create directory for Subversion repository files:
    sudo mkdir /var/lib/svn
  7. If you have any old repositories, copy them to /var/lib/svn/, and make sure the Apache user can read & write them:
    sudo chown -R www-data:www-data /var/lib/svn/
  8. Create Apache's Subversion password file with one user (replace username with one of your choice):
    sudo htpasswd -c /etc/apache2/dav_svn.passwd username
  9. Uncomment the following lines in /etc/apache2/mods-available/dav_svn.conf to point Apache to your repositories: 
    <Location /svn>
  DAV svn
  SVNParentPath /var/lib/svn
  AuthType Basic
  AuthName "Subversion Repository"
  AuthUserFile /etc/apache2/dav_svn.passwd
  Require valid-user
  10. Disable the default site (it clashes with the SSL settings somehow):
    sudo a2dissite default
  11. Restart Apache:
    sudo /etc/init.d/apache2 restart
  12. Test (replace repository_name with an existing repository name):
    svn co https://localhost/svn/repository_name

Sources: