Liberal Judaism does not require a Get to be issued when a couple divorce. In addition, a Get is not required to be re-married in a Liberal Jewish synagogue.
Orthodox Judaism has developed, and maintains, elements of Jewish divorce that are unacceptable to Liberal Jewish values – one of which is the Get.
However, Liberal Judaism also recognises that some other denominations of Judaism do require a get and that some couples like to have one. In these cases, the Liberal Judaism Beit Din can arrange for this.
Liberal Judaism also offers a mutual sefer-k’ritut document of separation.
Liberal Judaism does not have any specific rituals relating to divorce.
Although nothing is required, divorce is a time when people might seek ritual (for themselves, rather than for halachic reasons). If you would like to mark your divorce with ritual, you should talk to your rabbi to create a ritual to mark this new chapter in your life.