There are not many computer typefaces available for the Deseret Alphabet. Most of the ones which are available still overlay the Deseret Alphabet glyphs over ASCII (or 8859-1) characters. This is a dangerous practice and one which I discourage.
Inasmuch as the Deseret Alphabet is included in Unicode, and has been since Unicode 3.1 was released in March 2001, production and exchange of text data for the Deseret Alphabet should be done using Unicode. Unicode is generally supported by most operating systems and major applications (as of September 2006), so this should not be an unreasonable burden.
Nonetheless, for the sake of people running older Macintoshes, I still make my Deseret Language Kit available, which can be used with Mac OS 7.1 through 9.2.
For cross-platform use, two fonts are listed at David McCreedy's Gallery of Unicode Fonts: James Kass’ Code2001 and MPH 2B Damase. Neither, thankfully, is based on the 19th century originals, which are not elegant by current typographic standards.
Mac OS users need not install additional fonts; Mac OS X 10.4 (Tiger) includes a set of Deseret Alphabet glyphs in the Apple Symbols font. These are, unfortunately, based on the 19th century originals.
For input, the situation is somewhat worse. The Deseret Language Kit includes a keyboard. Both Ken Beeseley and I are working on keyboard layouts for Mac OS X. I'm not aware of any keyboard layouts for Windows. In any case, both Mac OS X and Windows allow the input of arbitrary Unicode characters. On Mac OS X, this is most easily achieved using the Character Palette.
Overview of the Deseret Alphabet
The Book of Mormon in the Deseret Alphabet
The Deseret Alphabet and Unicode