About 10 years ago, my mom gave me a single potted string of hearts plant. I promptly killed it several times, but, while it's easy to drown, it is also quite resilient, and can be brought back to life even when nothing of it is left above the surface of the soil.

Since then, I've enjoying caring for it, and learning its ways. Ceropegia woodii (wikipedia) is a succulent, which means it evolved where water might be scarce, and tries to keep lots of it inside itself. This is why it's quite easy to drown.
I've also been propagating it for several years, and giving it away as gifts to many friends. This is a little guide to help you care for it, ressurect it, and even make more.
Keeping it alive and well
Some plants get yellow leaves that fall off, and upon googling why, you're usually told it was either overwatered, underwatered, too exposed to sun, or not exposed to sun enough. Really narrows it down.
Thirst
Strings of hearts luckily communicate their thirst in a clear enough way. You can test how it's doing with the Taco Test.
The Taco test is when you gently squeeze a leaf nearest to the soil, as if to make a taco from it. If it yields, and you manage to fold it more than a few degrees, it might be thirsty.
This won't be true for new leaves, even if they're close to the soil, or for plants that were just recently put into soil, from perhaps a nursery (more on that later), but if the plant has some length, then the leaves near the soil are usually firm, except when they start running out of water.
In the summer I water mine about once every 7-14 days, in the winter less. I don't time it, I just do the taco test. It's better to under-water them than drown them.
Weather and sunshine
I keep reading they don't like direct sunlight, but I also keep suspecting those articles were written by people from the U.S. where there are 300 sunny days a year and it's >30 degress 6 months of the year.
In Slovenia, they're fine outside. My living room is actually too dark for them, and that shows by them making longer pauses between leaves. Dense leaves mean happy plant, fewer leaves mean it's reaching somewhere else, in case life is better there.
Now, they're not actually an outdoor plant, in Slovenian terms. Heavy persistent rain can drown them, hail can damage them, snow will kill them outright. If it's less than 10 degrees at night, they will be sad, so don't put them out. But summer months are fine.
The only thing to keep an eye on is that if they're outside, they might need water every other day, or even every day if there's a lot of direct sunlight.
One other mistake I've made is have parts of the plant touch the dark wood of my window sill, which got so hot on the sun it singed it.
My mom has them outside in direct sunlight the entire summer, and then brings them in when it gets cold. Hers look better than mine:

Soil
Since it evolved where water might be scarce, the soil there usually also doesn't keep water very long. So it's used to drinking from water passing by, but not being surrounded by wet soil. If it is surrounded by wet soil for too long, it can start to rot, and fungal gnats might take residence in the soil to pester it.
So the soil should be such that it lets water out of the bottom semi-quickly.
Making more
One of the most fun parts of Strings of Hearts is that you can make more! A lot more, very easily.
You might be reading this because I gave you one of my hearts, and maybe you want to make more too!
There are at least 4 ways that I've managed to make more:
Butterfly method
This is essentially for mass production, and a very easy method. You take any length of a vine and take some scissors. Cut next to each leaf pair, keeping abotu a centimetre of vine in each direction of the leaf pair.
Place that little intersection on some wet soil (you can bury it a little), and keep the soil wet for several days, carefully adding water so you don't wash the plant away from the soil.
It will grow roots fro mthe intersection and begin growing upward. I've made entire trays of them this way, although a tray of 20 might only get 10 that succeed.
Cut it up and put it in water
Also not complicated, you cut the vine such the you have 3 or 4 leaf pair in the cutting, then you remove 1 or 2 leaf pairs from the vine (nearer what was the soil before you cut it) and place the part with removed leaves in water. It will start growing roots from the removed leaves. I like to wait until the roots are at least a centimetre, but sometimes I wait until they're several centimetres long in water, before putting them in soil.
But, if you don't want to wait...
Cut it up and skip the water
My mom does this, she puts them straight into soil after cutting. It seems to just work... I'm too afraid to try.
Plant the tubers
If the plant is having a nice time, sometimes the intersections will grow dry white pea sized balls on them. This is a tuber. You can just cut above it, and place it in soil, and it's a new plant.
Ressurection
If there's ever an accident, and the whole plant dies (usually leaves start falling off, and don't stop), don't worry. Worst case, you dig up the soil, and find the underground tubers. They're like mini potatoes, sized between a pea and an actual small potato. Those stay alive even if all the leaves fall off. Just put them in fresh soil and wait for new plants to come out.
Flowers?
If the plant is happy, it has little flowers, usually in the summer months.
I think you can probably make more from the flowers, but I've never tried. It seems more involved.
Get in line
If you would like a string of hearts from me, you can ask anytime, and you'll get a place in line for upcoming plants.