Well, it largely depends on the Goddess and the pantheon she's included in.
Devotional activities are varied. You could write poetry or prose about her, perform actions she's over (say crafts for Athena or growing plants for Demeter), read her myths, read about her traditional worship, do a devotional meditation (prayers instead of mantras), and so much more. Just get creative with it.
Instead of a physical shrine, you could run and "e-shrine". Pintrest and tumblr are great places to make one. Just create a blog, and every time you see something that reminds you of the Goddess, reblog/pin it.
For food offerings, (make sure this is okay) you could dedicate the first bite to her. You could also leave out a small portion of your meal for her. And even still, you could pour out some of your drink for her. While there are traditional offerings, as long as it's something given in respect, it should be fine.
Shrines, or altars, are places dedicated to a spirit or deity. Their construction largely reflects the person's aesthetics and associations the entity has. You could make it a little inconspicuous if you are creative. I've seen places dedicated to gods which just look like book shelves, change jars, and decorations. You can give offerings here, or have a separate altar to give any offerings and perform rituals. The distinction between a shrine and altar is small.