Welcome to the forums MelinDURR.
There is a lot of free software available for making and burning dvds. In part, it depends on what you are starting with.
If you have dvd-video that you have ripped to the hard drive from commercial dvds, you may have to compress it slightly to fit onto a regular single layer blank disk. For that you can use a program called DVDShrink. Just click on DVDShrink in this paragraph and it will take you to the download here at cdfreaks. Read some of the guides to using it at www.mrbass.org or www.dvdshrink.info or here in our Movie Copy Software forum under Guides.
Once you have it to the size to fit, you can burn to disk with a free burning program called ImgBurn. www.imgburn.com Look through their guides to using the program....those guides can be seen here: http://forum.imgburn.com/index.php?showforum=4
By the way, there is a dvd decryption/ripping program that is still being updated and is still free to use. It is called DVDFab HD Decrypter. It will continue to function for this purpose even after the trial for the main part of the program expires. You can find it here: http://www.dvdfab.com/free.htm
Now, if you are starting with avi files, or mpeg4, or something similar that won't play on all stand alone dvd players, you can convert them to dvd-video using a program like AVStoDVD or FAVC or DVDFlick. Those are all free, and each can give you a finished dvd ready to burn. They can even use ImgBurn automatically if you set them up to do that.
AVStoDVD, FAVC and DVDFlick are all easy to find via Google.
Now, one last comment. Many newer dvd players can handle avi files that are encoded with xvid or divx codecs. If that is what you have, you can probably just burn them to a dvd as plain data files and have them play on such a dvd player. This may not apply to your particular situation, but it doesn't hurt to know.