Having had an altar (or altars) of one sort or another for quite a while, I know too well that it can be much easier to set up an altar than it is to maintain it.
So I will skim over the initial set-up discussion. You’ve got your flat space, you’ve got your statues or other god-images (or not), you’ve got candles maybe, offering bowls possibly. Perhaps an incense burner, divination tools, prayer book? And as time goes by, little gifts for the god or gods you honor at the altar. So, various altar stuff. Voila and well done! But if you’re using the altar at all, you will have to do some maintenance on it eventually.
Basic cleaning and dust removal. Statues tend to have lots of little ins and outs, nooks and crannies that tend to gather dust. You can wash some statues with water, but not all (as I and my favorite Hermes statue know from experience). I generally like to dust with a soft cloth, and I’ve come to really like those disposable Swiffer Duster things. (I don’t do this nearly often enough but I am always glad when I do it.)
The more items on the altar, the longer this will take.
Offerings of food and drink. If you’re offering food, or libations of wine, juice, milk, anything but water, then you’ll want to wash your offering bowls or cups after every use.
If you have a pest problem (no judgment there, in some seasons and in some regions this is unavoidable) you won’t want to leave food offerings out for too long, and you may want to cover liquid offerings to keep bugs and spiders out. Keep your climate in mind–don’t leave an offering of milk out too long in the heat, for example.
Altar cloths. I am actually torn on the subject of altar cloths. On the one hand, I have a lot of them, many of which I hand-knit in different colors (love those ombre yarns!). They can really pull an altar together and give it a more finished look; they are also a wonderful way to add some color symbolism to your altar or shrine.
That said, I really only use altar cloths for temporary altars I set up for rituals. For a permanent altar or shrine, I prefer a bare surface. This is at least in part because of the dust-gathering factor but it’s also because I like a more general-purpose look on a permanent altar.
Candles. Always assume that your candles will drip. Always assume that the drips will overflow the candle holder and onto the altar itself.
To get wax out of an altar cloth, everyone has their own favorite method. I like to stick it in the freezer and remove it once the wax has had a chance to harden (although with a textured altar cloth–like my hand-knit ones–even this is not a guaranteed success). Also keep in mind that a colored candle may leave a stain on the cloth even if you are able to get all the wax out.
I like to use a “candle coaster” sometimes, just a jar lid turned upside down, that can contain the drips. If I’m planning to burn a candle down entirely I’ll put it in a cauldron or other larger container.
Let the candle cool before you pick it up. I’ve had my hands bathed on numerous occasions with liquid wax from pillars, votives and tea lights, and ow.
Incense. I don’t use a lot of incense because there are folks in my household with a sensitivity to scent, but I do use it occasionally as an offering.
I like pressed Japanese incense that comes in sticks entirely made of incense. I like it because you can break it into smaller pieces and it burns just fine even if you don’t want to use the whole stick at once, which is nice if you are on a budget or if you’re doing a brief ritual.
I don’t have the fire-making talent to use granular or resin incenses, but you can get some nice traditional incenses (frankincense, myrrh, etc.) to use on charcoal.
You’ll probably want to clean out your incense burner after every use, or at least empty it out. Otherwise you’re likely to get a faceful of ashes the next time you pick it up (or maybe that’s just me :)).