In the past year I've had a venus flytrap and two sundews that each arrived healthy, flourished (and ate!) for a month or two, and then died (after which I tried again and bought a new one!). They all lived indoors in a sunny window. The care guide I received with them said to give them distilled water only, which I did. The plants were planted in small pots, with new sphagnum moss. I made sure the moss was kept moist to slightly wet at all times. I'd like to try again, as the sundews were super effective at controlling little gnats and fruit flies, but I'm worried about just killing it again. What am I doing wrong, and what should I be doing instead?
Of course it is difficult to know for sure, but it sounds like your general care is "the right type of thing".
Yes only use distilled water. Don't use "any old bottled water", mineral water, well water, or tap water. Rain water is generally considered acceptable but you might to avoid it if you have a lot of pollution in your area. Pollution generally translates into acid rain => increased acidity which is generally not a problem for carnivorous plants (CPs) as they prefer things a little acidic (alkali water and dissolved salts tend to be the problem). Serious CP growers invest in a reverse osmosis unit to create suitable water.
Do NOT let the plants dry out - they generally like things soaking - they are bog plants after all.
Do NOT feed the plants - let them do their own catching.
I would strongly recommend against buying them from a florists, or even the big box Home Depot/Lowes type stores. These places do not necessarily keep them in the best of conditions. Instead, go to a specialist, reputable carnivorous plant supplier. "Specialist" because they will know how to look after the plants. "Reputable" because you do NOT want plants from the wild, or imported against CITES (this is general advice - I assume you're in the US, so Venus Fly Traps are 'locals'!).
I would recommend the book I have from the days when I grew these: "Carnivorous Plants" by Adrian Slack, published by AlphaBooks in the UK. In the 90s it was the definitive guide - there may be other books available now.
I managed to grow Drosera (sundew), Dionaea (Venus Fly Trap), and Sarracenia (trumpet pitcher plant) from seed. These are probably the three easiest groups to grow. My main problem was laziness/forgetfulness to water. One of the Sarracenia (a hybrid variety) lasted about ten years and flowered.
Of the Drosera, I would recommend Drosera capensis. This is the most tolerant and it is a reasonable size (bigger than any Drosera that I've seen in the wild). It becomes a weed for the serious growers - readily spreading its seed into neighbouring pots!
Actually I find nepenthes easy to keep in a sphagnum moss and foam mix and nepenthes sanguinea or khasiana don't need terrariums at all also allow good drainage and water the Venus flytrap from below in a terrarium for the summer but in the winter cool it down so it can go dormant the drosera needs similar conditions but no summer terrarium as they seem to like it a little cooler and do well just in a tray of water. Also even though easy care I find sarracenia boring as as they don't don't grow in a very wild way just tall leaves and from a distance look like tall grass blades and often look frail. Although S. purpurea is cool looking with its tubby pitchers and all the bright red ones are cool too. Good luck growing