Have you already created a slideshow in Aperture (File > New > Slideshow)? Then use the "Export" button of the upper right corner to render the slideshow as a video file. Set the "Export for" pop-up menu to the format you need for the device where you want to watch the slideshow.
Once you have the video, you can either use the Finder to burn a data DVD from it (but that cannot be played in a DVD player) or use burn software to create a video DVD, that you can play in a DVD player. You will need special software to do this (Burn, iDVD), see this user tip for options:
And for a little Background reading Why is there no iDVD on my new Mac?: Apple Support Communities