A Paraclesis is a service of intercession to a saint that has as its main component a canon to the saint.
In the Slavonic tradition, a Paraclesis is usually called a "Supplicatory Canon" (Molebnyj Kanon). Unfortunately, in the Russian Church it has become somewhat rare to serve a full "Supplicatory Canon." What is much more common (and more popular) is to serve a "Moleben," which is in reality a very abbreviated version of the "Supplicatory Canon." The primary abbreviation consists in omitting the canon and chanting only the short refrains that would normally precede each troparion.
In the Greek Church, the Paraclesis is a popular service, and many have been composed to various saints. I remember being present at one in Thessalonica several years ago for St. Demetrios in his church there, where it was served regularly. It is customary in Greek churches to serve a Paraclesis to the Mother of God every day during the Dormition Fast as a way of preparing for the feast. This service is usually well-attended.
While the service of the Supplicatory Canon is rare in the Russian Church, it is not unheard of. There is an excellent recording of this service available that was made in Russia. In the diaspora, St. John Maximovich used to serve the Supplicatory Canon to the Mother of God during the Dormition Fast, and I have seen this practice kept elsewhere in the Russian Church Abroad.
The "Supplicatory Canon" to the Mother of God that is most commonly used in the Russian Church, is called the "Little Paraclesis" among the Greeks. There is also a "Great Paraclesis." These two are often used in an alternating fashion during the Dormition Fast. The canon of the "Great Paraclesis" also exists in Slavonic and is found as an appendix to the Octoechos. Unfortunately, it seems that it is rarely used.
The order of the service of the "Supplicatory Canon" in the Slavonic books is as follows;
Edited from a post to the "Ustav" mailing list
From: "Daniel Olson"
Date: Thu Aug 3, 2000 4:06 am
Subject: Re: [ustav] Dormition fast
We confidently recommend our web service provider, Orthodox Internet Services: excellent personal customer service, a fast and reliable server, excellent spam filtering, and an easy to use comprehensive control panel.