I've been providing tech support for more years than I care to remember, on both Mac and Windows. The panic call that I receive most often is "I can't find that file, and I need it now! Oh, and I can't remember what I called it." Great. Dandy. Sheesh.
Now, my physical desk and office are never neat, I admit it, but I've always tried to not let that extend to my computers. Organizing a computer is not that difficult, and it simplifies finding and backing up files.
Think of your hard drive as big filing cabinet. Each drawer represents a folder in that drive, one for Applications, one for Documents, one for System. Get the picture? There are subfolders in each of those drawers. My Documents folder (drawer) is broken up into subfolders for various categories, like MacGroup, business files, financial documents. The Financial documents folder is broken down by tax year. Is the picture clearing more?
Having the folder hierarchy in place and understanding it is only good as long as you use it. When you save a document, DON"T just blindly hit save. If all you see is a short menu when the save dialog box comes up, click on that little triangle next to the file name and you will have a much better finder window to work with. Click through to the specific folder for that document before you save. Even if you can't remember the name of the document or the date it was created, you have at least limited your search area.
If you are working on something that is going to take several sessions to complete, you can save it to the desktop to make it easier to find, but please don't leave it there. The desktop may seem like a good place to park things, but do it on a temporary basis only. The more cluttered your desktop, the slower your computer will run. When you finish with something, but it away in the proper folder. When you look for it six months from now, it will be much easier to find.
And before someone calls me out on it, yes, you will find more than one Application, Documents, etc. folder. You have the root level that gives access to all users on that computer, and you have User level which keeps files available to that user only. As you can see from the screen captures, I keep all of my applications and documents at root level. I'm the only one who uses my computers, and if I need to create a clean identity to troubleshoot problems, I still want access to my files. Use whichever you like, but be consistent.