You can connect the phone to the laptop - but not using Wi-Fi (Wireless LAN).
The laptop can connect to the phone and then connect to an isp (like FreeServe) using the modem built into the phone. This is essentially treating the mobile like a standard telephone socket - connecting you to the isp using the mobile and your mobile network. Therefore you can connect when you have mobile coverage.
You can 'connect' to the phone using the Infra-red link on the laptop. The mobile should be ready to go out of the box if you have Windows XP Pro. Just activate IR on the phone, make sure IR is active on the PC and point the IR ports towards each other.
The 610 also has Bluetooth - another method of connection that does not require a 'line of sight' connection between the phone and laptop. However, the A10 does not have Bluetooth so will need an adaptor (between £20 and £40).
All this connectivity is great, but can be slow and expensive. If you have GPRS, then connection speeds are almost as fast as a standard dial-up connection, but you normally pay per MB - check with your mobile network (anything from 50p - £3).
Wi-Fi is another story and has nothing to do with the mobile.
You can connect the A10 to Wi-Fi hotspots without a mobile. The laptop has a built in chip and transceiver that allows it to communicate with Wi-Fi access points. These hotspots have a short range - maybe a few hundred metres at most, and are not widespread in the UK yet. Click here to find out more on Wi-fi click here
Check your mobile network's website for details on how to connect the laptop. The Orange site is OK for some background.