How do I connect my laptop to the internet using wireless?

Most hotels nowadays offer a cabled ethernet connection or sometimes even a wireless connection for when you are traveling.  You can call ahead to find out what the hotels offer.  

You will not be able to get to the internet over wireless however unless you are connected to a cellular phone solution as mentioned above.  This type of solution is still growing as it is somewhat slow and impractical as of yet.

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What you will need:
To use wireless at home you will need a wireless access point.  Depending on your level of knowledge and configuration you may want to see if you can just simply switch the current router for a wireless router.  You can order a wireless router (pretty good one) for under 80 dollars online these days.  The wireless router will usually come with 4 ethernet ports in the back of it so that you can still connect your computer using the ethernet cable should you choose to.

You will need a wireless pcmcia card OR a wireless usb adapater.  In either case you will need to install some software for either one you choose in order to make windows work with it properly.  The wireless pcmcia card will be a really thin creditcard sized card that slides into your pcmcia slot on the side of your laptop.  It will have a built in antenna on the end of it that will usually look like a discolored extension of the car and will stick out a little further then you are used to.  It will also have a little link light on it to let you know when it can detect a wireless connection.  The usb wireless adapter is going to be a little bigger and it will have an antenna sticking up out of it (a normal looking antenna).  It will have a usb wire coming out of it that you will need to plug into your usb port on the laptop.  I have had more success with signal strength using the usb adapter as it has a larger antenna and can be somewhat moved/placed in different areas slightly away from your laptop.  Remember you only need the wireless pcmcia card OR the wireless usb adapter, not both.

That is all you should need equipment wise.  The configurations are generally pretty straight forward and do not require any special changes unless you run into difficulty connecting using the default settings.  This would enable you to connect your laptop wherever a wireless network is available (like the others said typically within 100 - 200 feet depending on the surroundings/material in walls/interference from 2.4ghz phones).
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How it works:  
Your computer sends information to your wireless card or adapter which translates it into wireless signals that radiate outward at 2.4ghz using the 802.11b (11mbps) or 802.11g (up to 54mbps!) (dont get 802.11a as it is not compatible with g) protocol.  The signal is relatively weak so it cannot pierce alot of walls and heavy materials... but it does go through new houses pretty easily and drywall etc  (expect similar performance to a walky phone, except static on the phone would be a good analogy for degraded performance of the internet for the wireless NIC).  The signal is picked up by the wireless router or access point (almost interchangeable terms for small home/office equipment) which then converts it back to the format needed to send it over the wires to your cable modem or dsl modem then out to the internet.
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If you are not at home around your wireless router (which stays at home btw), you will need to locate either a "hotspot" (alot of starbucks cafes offer wireless connections in their stores.  They use the same wireless routers you would at home connected ususally to a cable or dsl service), a hotel with wireless ability, or even some airports are going wireless as well.  Pretty soon it will be a standard for common business man areas to offer wireless solutions to help enable a truly "mobile" business world.

If you wish to go the cellphone route, it looks like there is some great info already posted!

GL

WhiteHawK