Don,

To try to address the questions as you framed them:

"The cable comes in through the wall. The man from Comcast attaches a signal splitter to the cable, hooks up one bit of cable to the television (as before) and another bit cable to a cable modem."

So far, so good. The cable is bringing signals into your house. The splitter allows you to send some signals to the TV and some to the cable modem, as you say.

"Now, if we just had the one computer..."

You could use a special Ethernet cable to connect from the cable modem to the computer. That computer would need an Ethernet connection ("Ethernet port," "LAN port"). Might be built in (looks like a wide version of a phone jack), or you might have to install an "Ethernet card" (circuit board). There are Ethernet cards for both desktop PCs and laptops. Desktop version would be $10 US or so.

"...a wireless network...cable from the cable modem would be hooked to a wireless router."

Yes -- though this would be true if you had, say, two computers in the same room and could connect them directly to a router. The router's job is to, um, route the signals to one or more computers.

My wireless router (D-Link DI-614+) can connect up to four computers, and it has four ports on the back, which means it could handle four wired connections, if the PCs could reach it.

"Install the essential software on each computer. The two notebooks came wireless-ready..."

They may have most of what they need to get to the wireless router, then. If the wireless cards are active, the notebooks should detect the presence of the wireless network -- once you've set it up, which usually requires a hard-wired computer (one directly connected to the router). Of course, you could use Ethernet cable (from the computer store) to connect one of the laptops to do the setup.

Depending on your configuration, if you have a computer in the same room as the router, you could hard-wire that computer to the router (hard-wiree: connect it directly with Ethernet cable).

"...but I'll have to do whatever is necessary to the desktop—wireless adapter? Is that a card I need to install?"

Your desktop machine needs a wireless card; it's the wireless version of the Ethernet card I mentioned earlier. Has a small antenna on it, to catch the wireless signal. Comes with software so the computer knows what's going on.

"Configure the software (not forgetting passwords, firewalls, anti-virus software, ad-blockers, and spyware removers!), and Bob's your uncle! "

You've got the big picture. Your cable company will probably have some install kit to help your computer recognize that it's now using the cable connection.

802.11b = older, somewhat slower wireless transmission rate. 802.11g = faster... but if you have one 802.11b device on your lan, then the overall throughput slows. I myself have 802.11b (i.e., slower). I may upgrade when the total cost of replacement drops below $40. Or not. I'm lazy.

Most important to remember is that the wireless speed is (a) theoretical and (b) computer-to-computer. Your lan will certainly be faster than your internet connection, which is nowhere near the 54 megabits of 802.11g.

(In other words, 802.11g lets you send stuff fast between wireless router and PC, but you don't get stuff any faster from cable model to router.)

The distance you can have a computer from the router is also theoretical -- walls, doors, floors, thickness of objects, solar flares all play their part. That said, I've been working away happily for about 18 months with no problem except when the cable goes out.

"Any recommendations?"

I have a D-Link router and a D-Link wireless card in the desktop -- others are fine, but I didn't want to mix apples and papayas. D-Link was very helpful when I set up the router. For what it's worth, I have a Linksys cable modem. None of this equipment has been any trouble.

Other advice once you get your lan set up, you want to make sure it's as secure as possible. You will have the opportunity to give your lan a name -- don't take the default name (HOME, MS HOME, LINKSYS, other clever names). Give it an odd name.

Next, look in the manual or the help file for the wireless router and see how to turn off SSID broadcast. SSID is the name of your lan; when I set my system up, the default was for the router to broadcast the name, which means anyone within range can see it's around.

After that, make sure you set up the wireless router with whatever wireless security comes with it (the default had been "leave key off," meaning, "don't bother with passwords"). Follow the manufacturer's suggestions, set up a difficult password (mixture of letters and numbers, don't name it after your dog, etc.).

This way, someone will need to know the name of your network (mine has a name from a language other than English), AND will have to know the password (the "key") in order to connect.

It's worth the effort. Hang in there. Expect some setbacks and expect to need the tech support people.