What you'll need
Here are some basics to keeping danios the right way and saving yourself and the danios lots of grief in the future.
Tank
You really should have a 20 gallon or larger, but you can get away with a 10 gallon tank. Danios are very active swimmers and thrive in longer (as opposed to tall, cylindrical, or hexagonal) tanks. They'll still survive in a tall 10 gallon tank and many people keep them in 10 gallon tanks, but if you're shopping for a new aquarium, go for a long 20 gallon.
Heater
Danios require a temperature of between 64-75°, but the important thing here is to minimize as much as possible the fluctuations in temperature. That generally requires an aquarium heater. A 50 watt stealth heater like the Visitherm is ideal. Note that this temperature is a little lower than what other tropical fish prefer, so keep that in mind if you are planning to add any tankmates.
Filter
You really need a filter for ANY fish, despite the fact people keep bettas and golfish in unfiltered tanks or bowls. But in this particular case, it is a must have. You simply cannot have a tropical fish tank without a filter. A simple sponge filter would be fine, or you could spring for something like a bio-wheel.
Lighting
Pretty self-explanatory. Some aquarium kits come with a hood that has a built-in light, but in case you are starting from scratch without a kit, just get very basic lighting. You aren't growing corals here where high intensity output is extremely important. The idea here is just to simulate day and night.
Water Conditioner
As hardy as danios here, you can't just put regular old untreatedtap water in the tank both initially and during water changes. Pick up Stress Coat or Prime- these are two extremely popular water conditioners that will get rid of chlorine so your water is safe to add to the fish tank.
Substrate
You need gravel or some type of substrate to line the bottom of the fish tank. Danios aren't picky, but if you're adding loaches or any type of catfish as a tankmate, you should stay away from rough ceramic media as this will scratch their faces. If you are adding live plants to the tank, then this is slightly more complicated in what substrate would be best. Standard issue aquarium gravel is fine otherwise.
Testing Kit
You will need the ability to test for ammonia, nitrites, and nitrates. Many people just use test strips, and these are fine for a guideline, but they're often not the most accurate thing in the world. Aquarium Pharmaceuticals makes a freshwater master test kit (which would also let you test pH), so that is something you may want to consider. No testing supplies available to hobbyists are 100% accurate...ammonia especially is a difficult test, so keep this in mind as well when taking readings. One other thing...many local fish stores and some chain pet stores will do a free water test, so you may want to confirm some readings with them.
Optional Items
You will probably want to decorate your tank, so any decor you buy, just make sure you rinse it off before putting it in the tank, as you don't want the water to get dusty. You might also consider a bacteria booster for starting the nitrogen cycle, though opinions are mixed on the effectiveness of these.