My homeschool organization has changed a lot over the years. I've had dedicated spaces and done school at the kitchen table. I've had whiteboards and chalkboards, and given them away. There's shelves and shelves of books and supplies of course, but how they are all organized has definitely depended on the space we had available.
To homeschool, you do need some kind of space, obviously. But you don't need a dedicated "school room" to homeschool. A lot of people try to recreate a public school classroom in their home, complete with desks, chalkboard, bulletin boards and all the decorations of a traditional classroom. And then they find that they never use it!!
Currently, in our new home, we have a semi-dedicated space. As my oldest has gotten older, and her school work more demanding, she's found it useful to have a desk that stares at the wall, and a dedicated spot for all her equipment - rulers, pencil crayons, protractors, her paints and brushes, etc. My younger girls all gather around me and my desk, so their school crates are in my home office, along with the shelves I have for school books and extra supplies.
You'll notice I said "school crates". Each one of my girls keeps their individual school books in plastic milk crates. Because each child is at a different level in school, they each have different books. The sturdy plastic crates help contain and separate each child's books, and still allow for a certain amount of mobility. Plus, they can be rearranged as necessary. They stack well, line up well, or can be left all over the room (or all over the house for that matter!).
As far as equipment is concerned, all you really need to homeschool is a place to write, a place to read and a place to store the books, treasures, pencils and supplies when you aren't using them. It's nice to have a desk for school, but you can just as easy write at the kitchen table. I would say some kind of shelf or cabinet is essential, but whether that's a kitchen cupboard set aside for craft supplies, a bookshelf in the living room, or an elaborate wall unit that is neatly labeled and organized, will entirely depend on how much space you have available .. and how organized you are as a homeschool parent!
It will also depend on your homeschooling style whether or not you have some kind of external writing spot, like a chalkboard or whiteboard. If you are a follower of the Charlotte Mason method, then you may want something you can write out copywork or dictation on. You may want a whiteboard to help practice letter formation with young children or show math problems and solutions to older kids. Some curriculum choices may also require you to have these available, either in large format or smaller individual sizes. For example, Handwriting Without Tears, a popular penmanship curriculum, uses individual chalkboards for the kids to practice making letters and numbers with, among other tools.
Another nice piece of equipment to have available for homeschooling is a dedicated computer or tablet, though obviously not essential. It is essential to have a computer of some sorts available, especially if you want your child to be able to learn typing skills, or have knowledge of how to use popular software, such as word processors and spreadsheets, or even to be able to research and find information online. But it's nice to have a dedicated system for the students, both for safety reasons (you can better control access to the internet, or if the computer will even have access) and for screen time reasons.
In my house, I have a personal laptop, for work and my blog (and, yes, I'll admit, my video games and movie watching), but I also have a dedicated laptop for my kids to do school on. My oldest listens to French on CD, and watches her Art lessons on DVD. My special needs second oldest has her own tablet, with specialized apps and softward designed to help support her weak areas and develop her strengths. With the separate computers, I can control screen time, and I don't have to fight with my kids over using the computer. (I do have to referee a few fights between them, however).
There are some special tools that may or may not be necessary, depending on your homeschool. We have a globe, but you could have an atlas, or just use some maps printed off the internet. Or none at all, if you aren't currently studying geography. When my girls were younger, we had a special calendar chart, with cards for the weather, seasons, the date -including the month and year and days of the week- and we currently use some weather tools, such as a thermometer and barometer, while my 6 year old is studying the weather.
Because we are Christian family, we have several Bibles around our house, and each of my older girls has their own to use for school. We don't currently use a flag or practice our national anthem, though maybe we should more often. If you want a flag, you can probably get one from your local
government representative, or just wait until the next national holiday and you'll find tons of affordable options in the store.
Other specialty equipment options may include more expensive tools such as a telescope or microscope. Again, these will depend both on your curriculum and study topic choices, and your interest level in those choices. Having a telescope is an awesome tool to have when studying astronomy, but, speaking from experience, it's absolutely not necessary either. We may consider getting a microscope in the future, though, since biology is a high school requirement here. Other science tools, such as prisms, magnifying glasses, binoculars, dissection tools, electrical kits, scales and measuring tools, chemistry sets, or anything else you may find useful are easily obtained as kits, from small-child-friendly to extensive and expensive options.
One of the best places I've found for the decor and informational items are the dollar stores. I've found great posters for the water cycle, the rock cycle, factors of weather, charts of animal kingdoms, plant diagrams, the solar system, or any other commonly studied topic there. I've also found amazing topical books and fun activity books there, along with dictionaries, thesauruses, and all the craft and school supplies I could need.
You don't need a lot of things to homeschool. But you may want a few things, depending on your space, lifestyle, philosophy and curriculum choices. And be prepared! Homeschooling is a messy business. Just check out my home office after a busy day of homeschool!