The most common thing I do is a small offering to Hermes. I have a shrine for him on a small wall shelf, which holds a candle, cone incense burner, a "Mercury-head" dime (it's actually Lady Liberty, but often assumed to be Mercury/Hermes, and seemed a suitable devotional object), and an image which I made by copying the Magician card in the Alchemical Tarot and mod-podging it onto a small wooden plaque (Lynda's suggestion, and a good one.)
For my usual devotion, I come to the shrine first thing in the morning, light the candle and recite (read) a prayer to him. Then I light a cone of frankincense and thank him for his favor. Sometimes I have a specific request to add, sometimes not.
I don't do this every day, but I miss it on the days when I don't.
On Wednesdays I often honor Woden, who was the first of the Shining Ones whose presence I felt in a way that seemed like more than wishful thinking. I do this at the main altar, with beer into a horn as a main offering. This too is something I'm being inconsistent about, though.
Once a month I have a "retreat day," which is part of ADF's recommended Dedicant Discipline for maintaining your practices after completing the DP. I'm blending it with the calendar of monthly libations at Hellenion to honor the Olympians at least one time each during the year. That involves a full core-order ritual honoring all of the Kindreds.
But we are dawdling on establishing the ancestor shrine we've discussed, and my offerings to the spirits of nature are sporadic. I have come a long way as a polytheist, as an ADF Druid, but there is clearly a ways to go yet.