New Camera Help - Depth Of Focus

I've recently bought my first Digital SLR, a Nikon D40 with 18-55mm
lens. The quality of pictures it's taking is great. I'm mostly playing
around with the preset scenes before getting in to the more
complicated settings. The only trouble I am having is with the depth
of field, I can get my object (person, boat, whatever) in focus but
everything else in the picture is out of focus, noticeably. Comparing
this with my Kodak point-and-click, I used to take a picture and my
foreground and background would both be perfectly focused
auotmatically but I can't seem to acheive the same with my SLR. The
following is a link to a picture taken with my point-and-click where I
have good depth of field but I can't see how to acheive this with my
new camera (http://www.trekearth.com/viewphotos.php?l=3&p=506700).
Any
advice on firstly, why this is the case and secondly, how to correct
it, would be very appreciated.

Thanks

Lee