What do we mean by online presence for networks? At the very minimum, we mean a website which can be created with little or no cost. If your network is not online, it is not accessible.
We strongly recommend that you use something like http://sites.google.com to construct and host your website. Apart from being free, it allows collaboration with multiple web editors and it gives you independence from any Institution. Being an online tool, it also allows you to edit your website from any computer with an internet connection without any special software being required. Alternatively, you could build a site with http://wordpress.com/.
A domain name can be obtained for less than 10 euros/year from providers such as http://joker.com/ (don't be put off by the name of the website). UACES will also create a short URL which can be used to direct people to the network website.
As well as traditional publishing in Journals and presenting papers at conferences, you can also disseminate research results, generate discussion and get feedback by blogging on sites such as http://ideasoneurope.eu/.
The Journal of Contemporary European Research is an online peer-reviewed journal and there are many others.
Consider using services like Jiscmail to set up an email list for your network, to allow your network members to communicate with each other effectively. Use your website to advertise the email list, so that new members can join easily.
Finally, if websites, blogging etc. are outside your comfort zone, remember that this is meant to be a network - delegate responsibility to someone who is keen to help!