How can I upgrade a Vista machine to windows 10 for free?

I don't have any serious goals for the Vista machine. I just want to use it as a simple game machine for kids.Vista doesn't work for some games so I want to upgrade to an operating system that could be used.

Ok.  Doesn't change that there isn't a free upgrade for it.

Install Linux if you want a free operating system.  

Or buy a refurbished system that will come with Windows 10 and probably play more games more effectively.

Lee makes an excellent comment about buying a refurbished system.  TigerDirect.com has all sorts of them for $100-200 that would likely be far more usable than something that originally came with Vista.

For example, $100 gets you a system with an I5, 4G RAM, 250G HD, and Windows 10 Home:
https://www.tigerdirect.com/applications/searchtools/item-Details.asp?EdpNo=630460&sku=42128927 

i agree wit the above; Vista type systems have too less Ram, and cpu power, and often too slow disk - and too little drive size - for getting a windows 10 to run smoothly on it; if my memory is right, they had 1 or 2 GB ram, while windows 10 requires at least 4, and better 8 GB , + a faster CPU 

There is no upgrade path to go from Windows Vista to Windows 10, because a lot of PC's that were running Windows Vista originally are not compatible with Windows 10, so even when the free upgrade period was in place, you could not upgrade from Windows Vista.

so - if you really want to move to win 10 on this pc, you'll need to backup everything, and do a fresh install

I can see from the comments that Windows 10 is not an option.

I have 4 computers and I don't need to buy another one. I just want to get some use out of the Vista machine. If I could find an install for Windows 7, that would be good as long as it's not expensive.

you should start by posting the specs first : cpu ram, disk, model....

I can see from the comments that Windows 10 is not an option.

That's not necessarily true.  Windows 10 is not a FREE option.  It really depends on the specifications as I alluded to in my first comment and nobus has specifically requested.

And as I said, you can always load a version of Linux.  Linux systems can have much lower system resources and Steam if available on Linux so some games may be available through it.

It doesn't seem that an upgrade to Windows 10 would be possible and Windows 7 would be unlikely. I am able to get some games working on the machine will just use it for those games that install easily.

I don't believe that Linux would work for Windows based games and I don't want to explore Steam based games now.

Nobus's comments are on the mark but Belarc advisor indictes about 2 gigs of Ram and a slow processor.

I'll just use it for whatever games I can get to run under Vista

You might be surprised.  It might not be REALLY easy, but Linux has some degree of emulation capabilities using things like WINe that can allow it to play Windows games.  

If this is a machine for the kids, learning linux is not a bad thing - you could be giving them an edge for the future.