how do i burn a slideshow created in iPhoto to disc?

What kind of DVD do you want to create? A data DVD with just the slideshow file, a movie file, on it or a video DVD that can be played on a TV set via a DVD player?

The latter requires the iDVD application. If your Mac came with Lion or later pre-installed you won't have iDVD as Apple discontinued iDVD over a year ago and will have to obtain it by purchasing a copy of the iLIfe 09 disk from a 3rd party retailer like Amazon.com or eBay.com. Why iLIfe 09 and not 11?

If you have to purchase an iLife disc in order to obtain the iDVD application remember that the iLife 11 disc only provides themes from iDVD 5-7. The Software Update no longer installs the earlier themes when starting from the iLIfe 11 disk nor do any of the iDVD 7 updaters available from the Apple Downloads website contain them.

Currently the only sure fire way to get all themes is to start with the iLife 09 disc:

This shows the iDVD contents in the iLife 09 disc via Pacifist:

You then can upgrade from iDVD 7.0.3 to iDVD 7.1.2 via the updaters at the Apple Downloads webpage.

If you only want to send the slideshow as a movie file export it out of iPhoto using the Export button and select the size you need in this window:

Then insert a DVD or CD disk in your optical drive and burn the file to the disk.

OT

What type of media and brand are you using? What burn speed did you choose?

Follow this workflow to help ensure the best quality video DVD:

Once you have the project as you want it save it as a disk image via the File ➙ Save as Disk Image menu option. This will separate the encoding process from the burn process.

To check the encoding mount the disk image and launch DVD Player and play it. If it plays OK with DVD Player the encoding was good.

Then burn to disk with Disk Utility or Toast at the slowest speed available (2x-4x) to assure the best burn quality. Always use top quality media: Verbatim, Maxell or Taiyo Yuden DVD-R are the most recommended in these forums.