According to scripture, he rides in on an ass unless the translators were overly mulish, in which case they seat Jesus on a donkey. But everyone does seem to agree that palm fronds were involved, hence the distribution of this foliage before Sunday's worship service.*
Can't speak for Christians in other denominations, but Roman Catholics (and I'm assuming Cradle Catholics who now worship elsewhere) get very excited by the distribution of palm fronds. Free stuff! And depending upon when, where and how they were raised, some getting even more excite about weaving palm crosses.
Do not try this at home. Repeat: do NOT try this at home. Palm crosses are meant to be woven during Mass/Holy Communion or whatever you call your liturgical main event. It is customary to wait until the homily/sermon or whatever you call what's happening from the ambo/pulpit or whatever you call the reading desk.
You should, however, practice at home so you can manage this folk craft without needing a flat surface, although you could use a hymnal. This video will show you how to make a basic palm cross:
* Eastern Europeans traditionally use pussy willow branches instead of palm fronds. For this and more info about ethnic-based traditions, check out my book: The Catholic Home: Celebrations and Traditions
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