Traditionally, a renku should start from the season in which you are writing it.
New Year's Season
Spring
Summer
Autumn
Winter
*
To give you an idea of what it will look like, see a sample renku.
Learn more: Mindful Renku: The Spiritual Journey of Linked Verse is both a survey of the history of Japanese linked verse and a how-to manual. Available as a paperback ($19.99), e-book ($3.99), and audiobook (check for price) at Amazon.