How can I burn a movie from iMovie without having iDVD

You don't have a PowerPC Mac in your signature. You posted to the PPC forum, which is for pre-2006 Macs.

If the problem is with the Mac in your signature, you need the hard copy iLife 2011 for iDVD, or the original discs that came with your Mac to reinstall iDVD.

If it is with an older Mac, tell us using Apple menu -> About This Mac what operating system you are running, and what iMac model you have.

See this post for several options including a free option.

https://discussions.apple.com/docs/DOC-3711

Why is there no iDVD on my new Mac? How do I get it and how do I install it?

https://discussions.apple.com/docs/DOC-3673

To burn a DVD with iDVD from the latest version of iMovie, you have to export the movie using the Export button and select 480p as the size. Open iDVD and start a new project, then drag that exported movie file into the iDVD menu window, avoiding any drop zones you see.

I had immense difficulty trying to burn a DVD from a movie after upgrading to iMovie.app in Mavericks. Previously I could share a completed iMovie project to Media Manager and then open iDVD and import it. Media Manager has gone, replaced by something called Theater. iDVD could not find my movie in Theater, nor anywhere in the iMovie library. I was able to save the movie as an mp4 through iMovie, but iDVD would not import this, claiming it was imcompatible. After wasting six hours of my time I re-imported the movie from the camera to Handbrake, which I then used to create another mp4 version. iDVD recognised this with no trouble.

I am a counsellor and need to video a client session once a year for supervision. This is the only time I use iMovie, so I need it to be easy, reliable and quick to use. The whole point of Mac OS is supposed to be that applications work seamlessly together and are easy and intuitive to operate. In my opinion the new iMovie fails on both counts. I agree with Klaus1's outrage that optical media are no longer supported. Most people I know still use them all the time.

You should still be able to call AppleCare for those discs. Apple initiated that model May 3, 2011, a full two and a half months before the release of Lion, and didn't discontinue it until October of 2012.