I have no clue on what the terminology I see being used means so PLEASE think of me as a first grader!!
well....we need to clarify some terms here....WiFi (in general terms) means a wireless connection between a wireless capable device and another wireless capable device...WiFi USUALLY refers to 802.11 traffic (a, b, g, or N) which is the standard used for device to device wireless communication over radio waves
a few things need to be cleared up as to what you actually want.
have dial up and I want to know how to get wifi-
it's not suggested to share a dial up connection (nor is it easy, or worth the effort)...more than one computer on a dial up connection would reduce the speed of the connection to a level so low that it would be quicker for you to get in your car and travel to where the owner's of the website live and ask them to read it to you instead of you trying to get there with your computer...
so you would want to upgrade to some form of broadband connection...the three most common broadband connections (depending on where you live) would be Cable (through your cable company), DSL (through your phone company), or Cellular broadband (through your mobile phone company)...Cable is the fastest of the three, and Cellular is generally the slowest (though you can reach low DSL speeds on a good cellular connection)... in some locations there is a service available called FIOS (from verizon) which is basically a fiber optic line directly to your house from the service provider which allows for REALLY fast speeds. you can also get satellite internet service(hughesnet) if you're too far out of range for any of the other options (very expensive and spotty reception in bad weather)
if you choose to get a broadband connection (do some research with your local providers and see what fits best for you as far as price and availability) you can either purchase an aftermarket wireless router from any computer store (or wal-mart) and follow the ISP (internet service provider) instructions on how to share the connection with it...or you can request a wireless capable modem with your broadband connection (usually costs more, and sometimes not as configurable by you)...this will allow any computer in your house with a wireless card to connect to the internet as well as each other (for file sharing, printer sharing, etc...)
for the laptop...how much traveling do you do? how light do you really want it? mac or PC?