When I was a child, my grandmother tied several layers of cloth over her kitchen water faucet to filter out sediments. That was our water filter, a home made water purifier, and thinking back, it's a wonder that we never were sickened by the spring water supply she used in her home, which was often contaminated by floods and upstream polluting by her dairy-farm neighbors. It used to be very common for people to make such home made water purifiers, and though the water at least looked cleaner, the method was very ineffective indeed.
Home made water purifier instructions you'll find online are complex. They are often simple filters, but they are often more complex systems such as distillation. Still, there are some serious problems with the do-it-yourself approach to water filtration. Improperly filtered water can be a health hazard. It is worth of praise and understandable that you wish to save money by making your own filters, but you should recognize that if you do, you may spend just as much money as you otherwise would while also putting yourself and your family at risk.
First, home made water purifiers generally don't tell you when they can no longer remove contaminants. Most professional grade water purifiers have some system whereby they will tell you to change filters or clean the purifier. Except for distilled water, you should assume that your home made water filter will need to be replaced, so you have to determine what the maximum safe use time for it is yourself. If you don't change the filter when it's saturated with contaminants, the result could be worse than if you used no filter, as fresh water running through will dissolve some of the contaminants already in the filter and give you a double dose.
Even if you use a distillation system or something else that supposedly removes all the contaminants from your water, you are likely to have a problem. For one thing, distillation removes even good minerals like iron, copper, and calcium, but it does not always remove chlorine, as chlorine is naturally a gas and will evaporate - and condense - right along with the water. In addition, distilled water that is not subsequently aerated will taste flat and lifeless, and your distillation system may add its own contaminants to your newly-purified water. You really need to know what you're doing.
If you're determined to do it yourself,a home made water purifier needs to have several layers of filtration in order to work effectively: sand or diatomatious earth, activated carbon, and layers of gauze or mesh to hold the filters in place. Water needs to be put through this filter at pressure. Then, at the end, you need to test the water yourself; the best way is to allow a glass of water to sit for a day or two and see what settles at the bottom or whether the water gets cloudy, and also test the water at biological laboratories for microbes and other things that can sicken you. It is likely to be cheaper and easier to just purchase a commercial system.