You have effectively asked for a full guide to DVD ripping which is a bit outside the scope of a post like this.
Still you have three main steps
1) Rip the DVD- many DVDs (which is to say most ones that are not put out by small groups) are copy protected. Fortunately laws conspired to make the decryption process painless for all should they have an even remotely modern machine.
Programs to do it
DVDfab
http://www.dvdfab.com/dvd-decrypter.htm
They do sell a lot of paid but like AV companies they have a free option that works just as well if you know where to look.
There are a few others but they might not work so well on some of the later DVDs and frankly the above program does well for it anyway. If we end up discussing DVD ripping in earnest then I will drop links all over the shop.
2) Get the part of the DVD you want (most likely the full film), for most DVDs out there* the decryption program can probably handle this part and there are other methods to do it as well. If you are good you can go directly from files and pull things apart but let us not go there right now.
If you do need such a method
http://www.afterdawn.com/software/cd_dvd/copy_dvd/dvd_shrink.cfm can do it for you.
*certain anime companies and cartoon/TV series DVDs do things slightly oddly here and will have one massive video with all the episodes end to end and tell it to jump to a point when you select the episode.
3) Encode this to whatever you want. I am not sure what the state of play is right now for straight DVD files of various forms to DVD- I tend not to watch DPG video and went manual for most of my encodes towards the end of that.
That said a quick look at
http://www.erightsoft.com/SUPER.html which ended up as the go to encoder for most people that wanted DPG video (and the alternatives were not that much better for most purposes) claims to handle it all which I can believe (
http://www.iwisoft.com/videoconverter/ also seems to have risen up in the DPG conversion world). I normally advise against it but if you wanted to rip to an AVI and then on to a DPG that can work well enough here (DPG was never great quality and here at least it does not compound the issue by going through two encodes, especially if you go for a bigger file size for the "intermediate" file).
How big.... as big as you want them to be really and if you drop quality they can be a bit smaller. Generally 300 megs or so for your average feature length film works reasonably well though can you probably go a bit lower. Frankly it is nothing that will worry a modern SDHC card if you just need a couple of films for a trip or to have in the case you need some time to waste.
As it tends to come up shortly afterwards- subtitles on DVDs are picture files of a sort it includes with the DVD. You need to either encode the ones that come with the DVD onto the image itself when you convert the video or you need to rip the subtitles to text and burn those accordingly. You might have to do the latter as the DS screen is not very big. I am not sure what the go to subtitle ripper is right now (subrip for basic ripping and then subtitle workshop, aegisub and subtitle creator to finish the job is my usual method here and a quick search says not much has changed though it was a very quick search).