I clean and lube my chain once a week. A guy at the LBS told me that once a week was overkill, but experience has taught me that regular chain cleaning saves you the pain of removing the chain, cleaning it in some solvent (diesel fuel works well, but it's not very green), dealing in similar fashion with the the equally trashed cassette & chain ring, and then reassembling everything. It's worth 15-25 minutes a week to not have to deal with all of that, and it's also nice to be able to pedal and shift smoothly/silently all the time.

What do you use to grease the chain?

When I was a teenager, I hated getting bike grease on my pants / skin etc so I liked it when the chain grease wore off.

I check my chain everyday before I ride, making sure that it's not too dirty or too dry. I only use "Singer Oil", cheap lubricant that is commonly used for lubricating Singer sewing machines.