What is your operating system, LO version, and file format? Are you are talking about using an audio file for slide transitions or embedding or linking an audio file in a slide? The former is done via Slide Show Slide Transitions... under the Modify Transitions section there is a Sound option which has an "Other Sound..." option in the pull-down. This should launch an Open dialog that allows you to select the required file. The latter is done via the Insert Movie and Sound... menu.

Please describe the expected and observed behaviour. It may be that you need to install the gstreamer- package to obtain the required audio support. As @zimmer points out in the comments below the gstreamer0.10-fluendo-mp3 package seems to provide MP3 support:

Record one sound file for each slide using some external program.

Then in LibreOffice Impress go to Slide Show → Slide Transition and for chosen transition method, by default No Transition which means nothing happens visibly, from Sound drop-down box select Other Sound..., locate recorded sound file for current slide and click Open. Do this for every slide you want to have narration.

After you set up your presentation you can see how it will behave in real-time and practice using Slide Show → Rehearse Timings.

John Wilson is correct according to page 163 of the documentation mentioned above.

"Note that Impress will only link the media clip, not embed it. Therefore if the presentation is moved
to a different computer, the link will be broken and the media clip will not play. To prevent this from
happening:
1) Place the media file, which is to be included in the presentation, in the same folder where the presentation is stored.
2) Insert the media file in the presentation.
3) Send both the presentation and the media files to the computer, which is to be used for the presentation, and place both files in the same folder on that computer."

Just a note, I'm not sure if the last line means you have to set up an identically named folder on the 2nd computer.