If you have iDVD it is fairly simple. Go to the File menu and select "One step DVD from file," select the avi you want to burn, put in a blank DVD when prompted, and wait. iDVD will convert and burn the avi, then eject the DVD and ask if you want to make another copy. If you choose to make another copy the process will be much quicker as it only has to burn again, but if you choose not to then decide later to do it iDVD will have to convert the avi again.
I've done this many times and had no problem playing the DVDs, but I don't have a blue ray player. Hopefully it will work for you, too.