Some new players will be able to read avi files encoded with xvid or divx codecs. Though even then, you have to set the parameters correctly that fit what your player expects.
Older players do not have this capability and need real dvd-video format. And dvd-video is still the most common and most widely supported format amongst dvd players.
To convert your avi file into a dvd-video, I'd suggest using one of either of these free tools: DVDFlick or AVStoDVD.
I prefer AVStoDVD because it is capable of higher quality output, but DVDFlick may be slightly easier to use for newcomers. Whichever program you use, make sure to set it to use NTSC format if you are in the US or Canada, or PAL format if you are from most anywhere else.
Download and install AVStoDVD. Go to Preferences-->Video and set it to NTSC. Save your settings. To import your avi file into AVStoDVD, click on the green + sign in the main window.
The final output from either of these programs will be a Video_TS folder and an empty Audio_TS folder. These are what are found in all dvd-video. You can burn the folders to a disk with most any burning program, but I prefer ImgBurn, which is also free. Both of these programs can be set to use ImgBurn automatically if you like.