Hi Michaelgtrusa.
I must begin my post by saying I do not condone illegally copying DVDs. Nowadays, a netflix subscription and the plummeting costs of DVDs (usually around $5 used if you know where to look) really has eliminated the need to illegally copy DVDs, however I have some knowledge that I am willing to share for purely scientific reasons.
One does not convert a copied DVD to a different codec. The data structure must remain the same if it is to play on a DVD player, computer, etc. What really matters is compressing the DVD content so that it will fit on the disk. Usually, this is not even necessary; if the disk is 4.7 GB (single layer) it does not need to be compressed for burning on a single layer DVD-R. Larger disks must be compressed in order to burn them onto single layer disks, but they can also be burned on duel layer disks (DVD-DL) without compression.
In order to copy a DVD, one must first copy the DVD content onto a computer's hard drive. An excellent tool for this purpose is FairMount, which tricks a mac into believing that a DVD is a removable drive. After FairMount is launched, the DVD disappears and reappears as a drive, and the VIDEO_TS and AUDIO_TS folders can be copied to your hard drive easily.
Now, you must burn this content. I maintain that the most useful program for this purpose is undoubtably Toast. Really, any recent iteration will do. To burn content, one must select the DATA tab, and check the box for DVD-ROM (UDF). Next, drag the VIDEO_TS folder AUDIO_TS folders into the window, ensuring that both folders are in a single folder (the disc) and that the disc has a title with all caps (e.g. LOST_SEASON_1_DISC_1).
Now click the big burn button. Toast should automatically compress the DVD content, burn it, and verify it. Now you have a disc that can be played in computers and DVD players alike. After you test the disk and make sure it's in good working order, you are free to delete the copied DVD content from your computer.
It's that easy. But it's illegal. Legal alternatives are cheap and numerous.
Happy experimenting.