It's probably heresy in the modern world of essential oils, but all I have is a small carved stone basin that sits atop a similarly carved, ventilated chamber holding a tea candle.
I have a ceramic tea-light powered one, with a removable bowl. I've always liked mine to have a LARGE bowl so that I can fill it up with water once, put drops of oil in - and leave it for quite a while. (the bowl maybe holds about a 2-shot glass amount of water). Shallow bowls run out quickly and one has to keep going back to add more.
(I always regret not buying a Kobashi burner when they were popular here. They had the largest bowls ever). I don't remember where my current burner came from... a tiny charity-like corner shop somewhere. Plus it didn't have a brand name either.
These ceramic oil burners are all I've ever used - actually nope, not true, I do like joss sticks too but not for the same purpose. I only have one with a removable bowl, and it is very handy, but I don't have any trouble washing the rest of them - soaking for a while in soapy water helps. Once, in the deeper bowl, I found the water boiling, which I assumed was because of its depth so since then I use that one with the same little amount as the others. I fill them as full as possible, just a tiny space for expansion as the water heats up. I am always careful to have the burner on a heatproof surface, but pretty blasé about all other precautions, but
of course I don't recommend or condone anyone following my example.
They tell you to burn them for a maximum of 20-30 minutes, which I assume is for safety reasons, though I have forgotten more than once and just found the candle burnt out, no harm done. If the water boils dry, and you've put a lot of drops of oil in, they do spit hot oil (though not very far) - but that too isn't supposed to happen either.
I usually put more than the maximum number of drops, and haven't had the house burn down yet; I think the maximum recommended is about 6? In fact I have a fear of fire, so I've cautious with the spent match, and dip it in the water before binning it, especially as I tend to use old cereal boxes and tissue boxes as table-top bins, which would be very flammable with a match smouldering unseen. It's more fun to dip the match "through" the oil on the water's surface, without blowing it out first... I am NOT recommending this, kiddies.
I do find burning an oil for half an hour scents the room nicely and the scent does hang around. Bigger rooms would need more than one burner, of course, and it's different when the windows are open.
I use lots of different essential oils and have a couple of little reference books on their uses, eg rosemary for aches n pains, and headaches, and staying awake if needed; lavender is well-known for relaxing and sleep (and headaches too); clary sage for concentration and clear-headedness; sandalwood for meditation; orange to improve appetite; tea tree when you've got a cold or similar bug... just off the top of my head... and cedarwood is excellent for getting rid of unwanted smells as opposed to just masking them (cigarettes for example, and I used to use it every time I changed a nappy(!) and for any other pongs, eg I couldn't find out what was making the sink smell and had people about to visit, so cedarwood did the trick until I identified the cause). If we're tending to bicker, I use ylang ylang which improves mood and helps get us laid-back instead of niggling about petty things - it's touted as an aphrodisiac, which I suppose is the same features, feeling friendly towards people and inclined to be happy!
I also use ylang ylang when feeling blue, not much use for full-blown depression, but if I have a day of being rather down without a reason - it really helps lift me. I recently found out that both clove leaf and peppermint are scents that spiders dislike so I fill the room with those to deter them - especially reassuring either side of the bed when one has been spotted in a corner of the bedroom! I witnessed a spider flee depart its own territory in quite a hurry after I sprayed with clove leaf essential oil (around the kitchen sink), so that definitely works.
The other way I like to use oils is in bathwater (most need some kind of carrier to be sure of not having a skin reaction, but a drop of bubble bath, or baby bath, or even shampoo under the running tap will do) - maximum about 8 drops in a full bath, if I remember right. Of course that scents the room beautifully too. The only oils that can be used neat, as far as I know, are tea tree - lavender, which I believe even fewer people react to - and geranium, which is handy for stopping bleeding. Its smell is too sweet for me to want to use it at any other time though! Lavender and tea tree are disinfectants and I always use a drop of lavender if a cut needs a sticky plaster. It's good for insect bites too, and eczema and that kind of thing. Rosemary is wonderful for aching muscles etc, but can be too fierce for sensitive skin so an oil burner would be better.
There you go, an info dump of my essential oil habits!