I have two computers,
(1) windows and dual boot linux slackware 14.2
(2) Mac laptop

In the past I used a piece of hardware to connect
a home network with two different computers. The
hardware was at times called a hub and sometimes
a router. It connected to the computers with
ether net cables.

Once again I would like to network my two above
computers, and could dig out that old thing
and plug everything in, I guess. But, I want
to use a wireless connection if possible and
not have the cables to hook up.

What do I need? All the wireless equipment I
look at has the ethernet connection ports on
them. None of them explain in their write ups
what is required. They just say mindless crap,
like make a home network with lightning speed
etc.

So what is some cheap piece of hardware that
I can network my computers with, no cables,
and transfer files between them?

You need a wireless router, pretty much any will do. Newer, more expensive models support faster protocols and more bands, but you'd have to provide more details on your laptops to know if that would be of any use to you. They will all have ethernet ports on them, usually one labeled WAN and 4 labeled LAN. If you want your computers to share an internet connection, you'd connect your modem to the WAN port. If you just want the two computers to talk to each other, you can leave the WAN disconnected. The LAN ports would be used for wired computers, but if yours are wireless you can ignore them*.

*When you first plug the router in, you'll need to plug one of the computers into one of the LAN ports with an ethernet cable to set up the router. Once it's set up and configured, you can get rid of the ethernet connection and just use wifi.

You may also be able to use one computer to broadcast its own wifi network that the other can join without any additional hardware, but that's a bit more advanced.

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