JACKie Sparrow, you didn't say whether your new digital camera is a point-and-shoot (p-n-s)or a Digital Single Lens Reflex (DSLR). I get the impression that you're a newbie, so I'm going to assume that it's a p-n-s.
There's merit to the other comments here regarding the differences between B&W film and digital B&W. There's also merit to the arguement that you may get superior B&W conversion by shooting in RAW format. However, if you just want a no-fuss method of getting B&W, and you're not particular about how professional the final results look, then here are some options.
Many p-n-s cameras have a mode or a menu option that allows you to take pictures in B&W, rather than color. Some cameras also have other "special effect" options, such as sepia, vivid color, cyanotype, etc. If the camera's built-in B&W mode satisfies you, then problem solved.
The problem with shooting in B&W mode is that once the camera saves the image in B&W, you can't change your mind about whether you would have preferred that image in color (this applies to jpg, not RAW). Most people prefer color for the majority of their pictures and are selective about the images they would like to convert to B&W. Therefore, I suggest that you shoot in color and convert to B&W using one of the following methods:
Many cameras come with software. The software bundled with your camera may have an option to convert a color image to B&W. If not, you can buy software or download free software (like Picasa) that enables you to do it. Another great free alternative is to use photoshop.com, which is a simplified online version of Photoshop. The nice thing about its B&W quick conversion is that it gives you different B&W versions, so you can choose the one that you prefer (if you want more contrast, less contrast). I highly suggest you give it a test drive.
Finally, many online photo printing services (snapfish, winkflash, shutterfly, etc.) offer B&W conversion. You just upload the color image and with the click of a button you can convert it to B&W. There are often other options like cropping, adding borders, etc. Then you can order the B&W print. Easy.
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