This isn't a carefully structured post - it's just a bunch of pragmatic info, in the hopes that it will be useful to people who need this information structured the way I do.
Camping is not a distinct activity with well-defined boundaries; basically it is going somewhere outdoors and staying overnight. Notwithstanding the flexibility of the category, there is an important difference between car camping and backpacking.
In car camping, you typically camp at a managed campsite within easy walking distance of a car. This means you can do things like pack a large cooler, and other not very portable equipment. On managed campsites there are typically amenities such as running water, sometimes even showers. The downside is you are typically adjacent to other campsites.
In backpacking, you walk a long distance to your campsite, which may not be reserved, and might just be wherever in the wilderness you happen to set up camp. Your equipment has to fit in a backpack which you’ll carry on the whole journey, so it needs to be much more optimized for smallness and lightness. There are specialized propane stoves and lanterns that can be useful.
You don’t necessarily have a standard “go camping” setup, though there will be some things you will often want to bring. Look up the attributes of the place you want to go, and expected weather, and develop a plan on that basis.
For sleeping, a sleeping bag provides temperature insulation from above and sides, but not from below, where your your weight will compress away the sleeping bag’s fluff barrier. Sleeping pads or mats generally provide insulation, as well as softness. Hammocks do not, and you’ll need an additional pad or underquilt. Bring a sleeping bag rated for 20 degrees F below the lowest temperature you expect to encounter at night.
The ground can be really hard. You probably need a soft sleeping surface.
There are lots of bugs in nature, especially when it is not very cold.
Tents are good for keeping crawly things off you, and also for keeping rain off you if you buy a tent that’s OK for rain (i.e. not one for “dry camping”). There’s a rain fly thing you can buy to put over a hammock, and separately bug nets, which I haven’t tried. Since it’s cool at night where I camped I didn’t have much trouble with bugs when I slept in a hammock. Some tents are designed to be good for backpackers, i.e. light and small. Car camping tents can get bigger and are generally a bunch heavier.
Hammocks don’t seem that great compared to beds, but they are a lot better than the ground, or inadequate sleeping mats. You get banana’d less if you sleep at an angle to the central axis of the hammock.
Pack food for calories and palatability. This is noticeably different from my experience house living, where calories just happen and I have to shop for meals and micronutrients. Don’t just pack for calories, pay attention to whether you’ll be able to stomach the implied number of servings of this one foodstuff. I bought a 5 pound thing of oatmeal for a two week stay in a cabin. I got tired of having more than a bowl of oatmeal a day, and had to go pick up more groceries. Bread turns out to be pretty awesome and versatile. I got less tired of tinned fish than I expected.
Have somewhere/something to store your food in, that is hard for animals to get into, otherwise they will get into it. Animals are generally not very considerate about leaving your food in carryable shape the next day, and probably you will want to abandon the food bag they broke into and rummaged through anyway.
You need water. Have a plan for getting access to water. If you won’t be at a site with potable water taps, check where there is running water nearby and if so whether you’ll need to filter it.