Jumping spiders are probably the easiest invertebrate to recommend to someone who's never kept one. They're small, their care requirements are genuinely simple, and they have a quality that most invertebrates lack: they look at you. Those oversized front eyes (the anterior median eyes, if we're being proper about it) give them a face that people respond to, which goes a long way towards making them feel like pets rather than terrarium residents.
I've kept jumping spiders on and off for years, mostly Phidippus regius and a few Hasarius adansoni. Here's what I've learned about keeping them well.
Enclosure
Jumping spiders are arboreal. They want to be up high, and they'll build their web sac (a silk retreat where they sleep and moult) at the highest point available. This means height matters more than floor space. A well-ventilated container about 15-20cm tall works for most adult specimens. For slings (spiderlings), something smaller is better because they need to find their food.
Cross-ventilation is important. Mesh on two opposite sides prevents stagnant air and mould, while still retaining enough humidity for the spider to drink from droplets on the walls. Purpose-built jumping spider enclosures with front-opening doors are widely available now, but a modified sweet jar or deli cup with mesh ventilation holes works just as well for less money.
Add some fake plants, a stick or two, and maybe a bit of cork bark. The spider doesn't need much in the way of decoration, but a few climbing surfaces and some visual complexity seem to make them more active and interesting to watch. They're visual hunters and diurnal, so placing the enclosure somewhere with decent natural light (not direct sunlight) keeps them on a proper day/night cycle.
Temperature and humidity
Room temperature in a UK home (18-24C) suits most commonly kept species perfectly. You don't need supplemental heating unless your house is particularly cold in winter. Jumping spiders are tolerant of a wider temperature range than many invertebrates, though they'll be less active at the lower end.
For humidity, mist the enclosure walls lightly every couple of days. The spider will drink from the droplets. Don't spray directly onto the spider because water droplets can trap small spiders, especially slings. There's no need for a hygrometer. If the walls dry out completely between mistings, you might want to mist a little more frequently. If there's condensation constantly dripping, you're overdoing it.
Feeding
Jumping spiders eat live prey. There's no getting around this. They're visual predators that need the stimulus of movement to trigger hunting behaviour. Dead or pre-killed food won't interest them.
For slings and juveniles, fruit flies (Drosophila) are the standard. Flightless or curly-wing cultures are easiest to manage because you can tap a few into the enclosure without half of them escaping into your kitchen. As the spider grows, move up to small houseflies, greenbottles, or bluebottles. Adult Phidippus regius can handle small crickets and waxworms, though I find flies are the most reliably taken prey.
Feed juveniles every 2-3 days and adults every 3-5 days. They'll sometimes refuse food, especially in the days before a moult. This is normal. A spider that hasn't eaten for a week but has a plump abdomen is almost certainly preparing to moult, not starving. Leave it alone.
Remove uneaten prey within 24 hours. A cricket left overnight can harass or even injure a moulting spider. This sounds paranoid but it happens more often than you'd think.
Moulting
Jumping spiders moult multiple times throughout their lives, shedding their old exoskeleton and emerging slightly larger each time. Before a moult, the spider retreats into its web sac and stays there for anywhere from a couple of days to a week. Don't disturb it. Don't open the web sac to check on it. Don't feed it. Just leave it alone.
After moulting, the spider will be pale and soft for a day or so while the new exoskeleton hardens. Don't feed during this period either because the fangs need to harden before the spider can handle prey. Give it another day after it emerges before offering food.
Failed moults are the primary cause of death in captive jumping spiders. They're usually caused by insufficient humidity (the old exoskeleton doesn't separate cleanly from the new one), disturbance during the process, or insufficient space to hang and stretch while moulting. Ensuring good humidity and leaving the spider undisturbed during this period are the best things you can do.
Handling
Most Phidippus species tolerate handling reasonably well once they're adults. They'll walk across your hands and seem curious rather than defensive. That said, they're fast and fragile. A fall from hand height onto a hard floor could kill or seriously injure them.
If you want to handle your spider, do it over a bed or table, close to the surface, so any jump or fall is onto something soft. Coax the spider onto your hand rather than grabbing it. And be prepared for sudden, surprisingly long jumps. They're called jumping spiders for a reason.
Slings and juveniles shouldn't be handled. They're too small and fast, and the stress isn't worth it.
Lifespan
This is the difficult part. Jumping spiders don't live very long. Females of most commonly kept species live 1-3 years. Males live less, often only 6-12 months after reaching maturity. For Phidippus regius, expect roughly 12-18 months for a female from the time you acquire a juvenile, and perhaps 6-10 months for a male.
There's nothing you can do about this. It's their biology, not a care failure. It does mean that if you get attached to them (and you will, because they have more apparent personality than almost any other invertebrate), losing them feels disproportionately sad for such a small animal.
Common problems
Beyond failed moults, the most common issues are dehydration (make sure you're misting regularly) and injury from live prey left in the enclosure too long. Both are entirely preventable.
Jumping spiders are solitary predators. Housing two together will result in one spider. The only exception is very brief, supervised mating introductions, and even those carry risk. Always keep them individually.