"Sepia Bee," f/5.6
Shallow depth of field is one of the first things you learn about in Photography 101 and I won't get into all the technical stuff (but you can learn more about it here), I'll just skip to how you do it.
With automatic cameras it can be hard to achieve since they focus automatically but the little flower symbol is the Macro setting intended for close-ups so try that. For those with a few more setting options, set your camera to "Av" (Aperture Priority) and scroll it down as low as it will go, for most standard lenses f/5.6 or f/4, etc. Then get as close to your subject as you can so that the focus is on the object. With this shallow depth of field, the object close to you should be in sharp and in focus with the background nice and soft.
"Morning Pink," f/4
This method is wonderful for portraiture and if it's something you think you'd like to do more of, consider investing in a macro lens or one with a crazy low f-stop like 1.4. They can be expensive but the images they produce will not disappoint.
Need more inspiration? Blogger dooce loves using the shallow depth of field in her gorgeous family portraits. Also professional photographer Me Ra Koh is a frequent bokeh creator in her stunning wedding photos. There are also a ton of groups on Flickr dedicated to the beauty of bokeh.
Have fun experimenting and if you have any questions about depth of field or photography in general, please let me know!