Setting aside enough food for a family of four to last just a few weeks takes up a fair amount of space, let alone planning for several months. Not everyone has a huge walk-in pantry to use either.
Basements are usually good places to start, as long as they are dry. Use a dehumidifier if need be to keep moisture out of the area. Build simple shelves from 2x4s to keep things off the floor and organized. Do NOT use the cheap pressed board bookcases you find at discount stores. The shelves will warp rather quickly under the weight of canned goods.
If you have staircases in your home, do you have access underneath them? There are many different plans available online for building various types of shelving to take advantage of this often unused space.
I’ve heard of some folks who built shelves inside their walls, using the space between the studs. This isn’t a bad idea, as long as you can easily access the food stored there so you can rotate it regularly.
Most beds have a fair amount of space under them, enough room for at least a few cases of canned goods.
Check your closets and see if there is enough space along the back of them to install some shallow shelves. For canned goods, they only need to be 5″-6″ deep.
For apartment dwellers, you probably have a small storage unit of some sort in the basement. You could box up your food storage items and label the boxes “Old Clothes” or something else innocuous. Go a step further and put a couple old shirts over the top of the food in the boxes.
Remember, store what you eat and eat what you store. Rotate, rotate, rotate. The food won’t do you much good if it goes rancid or is otherwise unfit for consumption when you most need it.