With the school of Zen I am familiar with you pretty much do "just sit". The practice is called Shikantaza, literally "Just sitting" in english. With 10% chanting and bowing afterwards.
AFAIK, Shikantaza is only done after you've had a good amount of experience with other, more structured forms of meditation, like counting breaths or following the breath. At this point, you should already have some idea of where you're going, and "just sitting" will be more than just sitting to you.
I sit at a Dojo regularly and occasionally do introductions. We don't teach counting, but do teach following the breath at the nostrils and settling the mind in the hands, as things to come back to once the mind has wandered. There is some technical stuff about posture to learn but basically you just turn up and sit. If they do it differently somewhere else that's cool too, lineages vary.
