As for the actual "how to do it", I'd do some the following:
* Do some research on basic gear to take (tents, water treatment, first aid, etc)
* Hit up a place like REI, Mountain Equipment Co-op or similar and load up. Make sure your boots fit - most good stores will have an incline you can jump around on to make sure your foot doesn't slip in your boot. Make sure you get the correct size of backpack, although this is not as critical as properly fitting boots. As a general rule, spendier stuff will either be tougher material or lighter, but you don't need to go nuts unless you're overburdened with cash.
* I'd start with a simple out-and-back overnight hike. If you're being careful, which you should, you'll probably have overprepared and will have a heavy pack, so a longer trip might not be fun. Over time you'll probably start to tweak what you take, get better gear and so on, and and your pack will start to get lighter. You'll also presumably find yourself getting fitter.
Backpacking is one of my favourite things to do on this earth. All your concerns with work, possessions, relationships and so on fade away, and you find yourself just focused on getting to the next camp, enjoying the wilderness and whatever company you have, finding water, and so on. It's an incredible experience.
Don't feel obliged to spend up on boots. I have done a fair number of multi-day hikes in various countries wearing a pair of low-cut hiking sneakers (Nike ACG All-Trac something) and my brother wears regular ASIC runners. Unless you're in snow/mud or a bit clumsy with your ankles, sneakers are lighter and more flexible in my experience.
And even those shoes have handled snow/etc fine for me though if you're hiking deep snow in the US it might be a different story.
There are loads of great day hikes (especially in the US) to test out things generally before you commit to a tent, camp stove, etc.
Backcountry hiking is great fun, but you don't need to hike out into the wilderness to find good darkness. You can instead visit an astronomy club on their way to a "dark site". Look that up and see if you can find one near you. They are usually not more than a few hours drive away, although if you are on the east coast it make take more travel time.
Or just get in your car, drive until you are really far away from anywhere, pull over, and look up. Then go find a motel.
Start doing research about gear you will need for backpacking and where to go near you. State parks are great places to backpack. It took my SO and I about 3 months from initial research to take our first trip. I absolutely love it and also go several times a year now.
Just remember to take it slow! Always better to be over prepared than underprepared. Mother nature is not forgiving.
This is good advice. Start slow (short trips, close to civilization) and build up over time. Your experience will tell you what gear you need much better than any review site.
One of the best places to actually START is just Google up a local park, grab a water bottle and do an out-and-back (e.g walk 15 minutes along the trail and then turn around and retrace your footsteps back to the trailhead.) You can do this over lunch.
Great advice, especially with starting with super short trips. One of the most important things is clothing and these short trips will let you figure out a good set of shoes, how to layer clothes etc, without putting you at risk of being shivering cold with blistered feet in the middle of no where.
When you're in town, you can't see it. When you're in the backcountry, you can't NOT see it.