If the camera and laptop both have USB connectors that is one way. Most cameras will come equipped with a suitable USB cable
By digital camera I'm assuming you mean a stills camera rather than moving images. If you mean moving images then your best bet is via a firewire (IEEE 1394) connection.
The reason the pros look at their pics on a laptop is to get a better look at the shot before sending it to the newspaper picture editor rather than relying on the tiny screen on their camera. The laptop is used to send the image either by bluetooth to a mobile and then to the paper or using a wifi hotspot then via the internet.
As for cameras you can spend as little as �50 on a Nikon snapshot camera at Argos or as much as �1500 on a full blown Nikon digital SLR. What you will need depends on what type of pics you want to take. SLRs offer the best fuctionality and flexibility as you can change lenses over, wide angles for interior or landscapes or telephotos for sport and wildlife.
Check this website for some reviews of all types of cameras (it's American but does links to uk sites for the prices)
http://www.steves-digicams.co.uk/
Best of luck