Mistress Honnoria, of Aethelmarc, sent me the following link about using oil lamps.
Placed wicks are those simply placed in the oil, with one end resting on the bottom and the other end resting on the edge of the lamp, outside of the oil. This outer end is what is lit, and burns as the oil is drawn up the wick. This is a very simple arrangement, but suffers from the drawback that since the flame can only burn on the upper side of the wick, the oil on the lower side generally drips down the outside of the lamp. It was common to place the lamp on a saucer of sorts both to protect the table from oil stains, and to recover the oil for reuse.
Okay, I need saucers.
Also, apparently the lamp is partially filled with water for economy, a cotton mop head is recommended for economy (though lots of other wick materials work too).
He also mentions lamps made of glass (which we've all seen) so perhaps my lamps being glazed won't affect their function after all.